The randomized variable's sample distribution would be as follows: H+/- 1.96 * √3)/√n
A random variable in mathematics would be a variable for whom the value is the numerical result of an unpredictable event and a random number generator X on a sample space. S denotes the rule that gives each of the outcomes S in a collection a numerical value.
In this case, we have assumed that x is a constant random variable with values ranging from 0 to 3, but we are unsure of its distribution, mean, or variance.
The mean of x, which we designate by the letter h, is what we're now interested in estimating. To provide a conservative estimate (upper bound), we'll choose 1.5 for the standard deviation of x.
In this case, we must estimate h. To do this, we select the sample size n, the samples x1, x2,.., xn, all of which share the same dissemination as x, and accurately measure the sample mean.
Therefore, we have used a normal distribution to determine the variation of x as (0,6),
And it equals to 3, then apply CLT resulting in
=> H+/- 1.96 * √3)/√n
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A tablet that regularly sells for $330 was
on sale for 15% off. If Jeremiah paid
$302.94 total including tax, what is the N
sales tax rate?
Answer:
The sales tax rate is 7.96%.
Step-by-step explanation:
To determine the sales tax rate, we need to first calculate the amount of the discount on the tablet by multiplying the regular price by the discount percentage:
Discount = Regular price * Discount percentage
Discount = $330 * 15%
Discount = $49.50
Next, we can calculate the total price of the tablet before taxes by subtracting the discount from the regular price:
Total price before taxes = Regular price - Discount
Total price before taxes = $330 - $49.50
Total price before taxes = $280.50
Finally, we can calculate the sales tax rate by dividing the total amount of taxes paid by the total price of the tablet before taxes and multiplying by 100% to express the result as a percentage:
Sales tax rate = (Total amount of taxes paid / Total price before taxes) * 100%
Sales tax rate = ($302.94 - $280.50) / $280.50 * 100%
Sales tax rate = $22.44 / $280.50 * 100%
Sales tax rate = 7.96%
Therefore, the sales tax rate is 7.96%.
for what natural values of n are the value of the following expression equal to a natural number: 36-n^2/n^2
Answer:
All natural numbers
Step-by-step explanation:
I'm assuming that you mean 36-(n^2/n^2)
A natural number is a positive integer
n^2/n^2 is always 1 for natural numbers.
so 36-1=35 which is a natural number
in certain areas of the city, the Electricity power is cut randomly in a rate of 3/day find the probability that in any given day there are at least 7 cuts at most 4 cuts.
Answer: This comes out to be 0.1031.
Step-by-step explanation:
in this case, we are given that the rate of power cuts in the city is 3/day, so the rate parameter for our Poisson distribution is $\lambda=3$. We want to find the probability that there are at least 7 cuts but at most 4 cuts in a given day. This means we need to find the probability that $k=7$, $k=8$, $k=9$, ..., $k=4$. We can use the formula for the probability mass function to find the probability for each of these values of $k$ and add them together to get the total probability.
Simplifying assumptions identified for the use of cost behavior pattern data include:a) linearity and relevant range.b) fixed range and variability.c) fixed activity and linearity.d) relevant range and liquidity.
linearity and relevant range include the use of cost behavior pattern data.
what is linearity?the existence of a chain of thoughts or actions wherein one directly follows another: True autobiographies rarely have a linear structure. We don't have a linear existence. Constantly thrown off balance is the narrative's traditional linearity.
what is relevant range?The accounting phrase "relevant range" refers to the production or activity parameters that a company must adhere to in order to keep its fixed costs constant. Fixed costs in accounting are constant and unaffected by particular production rates.
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______ is thermal energy that is transferred from something at a higher temperature to something at a lower temperature.
a.Heat b.State c.Plasma d.Charge
Answer: Heat
Step-by-step explanation:
Heat is thermal energy that flows from something at a higher temperature to something at a lower temperature.
Answer:
it is heat
A
Step-by-step explanation:
among all option it is only heat that is a thermal energy
HEAT is thermal energy that is transferred from something at a higher temperature to something at a lower temperature
ADDITIONAL INFORMATIONS
state means the particular condition that someone or something is in at a specific time.
plasma means the colourless fluid part of blood, lymph, or milk, in which corpuscles or fat globules are suspended.
charge means is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
PLS RATE ASBRAINLIEST
1. A study explored the effect of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 was water (control). Treatment 2 waas 1g of ethanol per kg of body weight, and Treatment 3 was 2g/kg. The amount of REM sleep (in minutes) in a 24hr period was recorded: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
(a) Graph the data. Why did you choose the graph that you did and what does it tell you?
(b) Create an ANOVA table for the data using the formulas provided in class. Show your work. You may use R to check your answers.
(c) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?
(d) Based on the ANOVA table, make a conclusion in the context of the problem.
(e) Create 95% CIs for all pairwise comparisons of means using the Tukey method. Do this without R show your work. (You may use R to check your work). Summarize your results using letter codes. What do you conclude?
We have to find a problem at the 5% significance level.
Sample size = 10.
We're losing one till test if the Significant value is at five and 10. The critical value of W. C. is 44. When we look at the test, we're supposed to do one tailed. Which tail is it?
We are asked if one is more effective than the other.
Everything is mostly positive here, and we find what our values are. Mhm. 10 patients who used love level high school obtained additional sleep hours by using the following data set High bromide.
That's the control group minus the other one.
The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.
The other tail is going to be divided by two and the right tail is going to be 44. 55 minutes 44 is going to be 11. It's very handy. Okay. If it's less than 11 it won't reject and if it's greater than 44 it will reject. Is it sound good? We had 10 students who were at the positive values and they were 1.9 plus 0.8 plus 1.1 plus 0.1. We get 23.4 for our nut. Okay. Critical value leads us straight to the middle. We failed to reject the null hypothesis and this was just a right tail test. If we tried it again at the 1% significance level, it would change our values to be 50. We did 10 tons 11 divided by two. Fifty is going to be five. Again, 23.4 lands us right in there.
We failed to reject the hypothesis again.
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3) Sally is in a long-jump competition. Her first jump is 5.7m. Her second jump is
6.2m. What is her percentage increase in jump length?
The percentage increase in her jump length would be 8.77%.
What is a percentage increase?
The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in percentage.
The initial jump was 5.7m and the second jump is 6.2m
By using the percentage increase formula, we can write
Percentage increase = (final value - initial value)/|Final value| * 100
= ((6.2 - 5.7)/6.2)*100
= 8.77%
Hence, the percentage increase in her jump length would be 8.77%.
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Question 1. An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Over Age of 18: n1 = 500 Number of accidents = 180 Under Age of 18: n2 = 600 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is Pu-Po = 0 Pu-P. £0 Pu-P.10 Pu - P. 30 Question 2. Refer to Question 1. What is the value of the pooled proportion? Round your answer to three decimal places.
Question 3. Refer to Questions 1 and 2. Determine the value of the standard error of the difference in the proportions. Round your answer to four decimal places.
The pooled proportion is 0.200 and the standard error of the difference in the proportions is 0.0201.
1. The null hypothesis is Pu-Po = 0, which means that the proportion of people under 18 who had accidents is the same as the proportion of people over 18 who had accidents.
2. To calculate the pooled proportion, we first add the total number of people in each group (500 + 600 = 1100). Then we add the total number of accidents in each group (180 + 150 = 330). Finally, we divide the total number of accidents by the total number of people to get the pooled proportion (330/1100 = 0.200).
3. The standard error of the difference in the proportions can be calculated using the formula SE = SQRT(P1*(1-P1)/n1 + P2*(1-P2)/n2), where P1 is the proportion of people under 18 who had accidents, P2 is the proportion of people over 18 who had accidents, and n1 and n2 are the number of people in each group. In this case, P1 = 150/600 = 0.250, P2 = 180/500 = 0.360, n1 = 600, and n2 = 500. Plugging these values into the formula gives us SE = SQRT(0.250*(1-0.250)/600 + 0.360*(1-0.360)/500) = 0.0201.
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a movie production company is releasing a movie with the hopes that many viewers will return to see the movie in the theater for a second time. their target is to have 40 million viewers, and they want more than 40% of the viewers to want to see the movie again. they show the movie to a test audience of 140 people, and after the movie they asked them if they would see the movie in theaters again. of the test audience, 66 people said they would see the movie again.
As per the concept of hypothesis, the value of p is 0.47 the value of the static hypothesis is 4.3893 and the statistical division when the alpha = 0.05 is 0.1085.
What is meant by hypotheses?
in math, hypotheses refers a an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
Here we have given that, a movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a 2nd time. The target is to have 40 million viewers and they want more than 40% of the viewers to return to see the movie again.
And they show the movie to a test audience of 140 people.
Of the test audience, 66 people said they would see it again.
And we have to determine, the p-value is, the p-value for the test statistic.
And the statistical division when the alpha = 0.05 and explain the managerial conclusion for this situation.
Based on the question, the null hypothesis is,
H0: P = 3
H1: P > 0.03
Here we know that they show the movie to a test audience of 140 people.
So, n = 140
Here the test audience, 66 people said they would see it again.
So, x = 66
Therefore, the value of p is,
=> 66/140 = 0.47
Then the test hypothesis is,
=> Z = (0.47 - 0.3) / √[(0.3(1 - 0.3))/140]
When we simplify this one, then we get,
=> Z = 4.3893
Therefore, value of the static hypothesis is 4.3893.
Then the p-value = 0.1085 at 5% level of significance.
Here, 0.1085 < 4.3893,
Therefore, the null hypothesis is not rejected.
Therefore, p-value = 0.1085, and we will not reject the null hypothesis.
So, the value of the static hypothesis is greater than the null hypothesis and the value of p so the value of not rejects the null hypothesis.
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Refer to Exhibit 1-3. According to the data provided in this table, what is the approximate slope of the line between points A and B, if these data were graphed with X on the horizontal axis and Y on the vertical axis?
-0.29
The slope of the line between points A and B based on data provided in the table is -0.29. (Option A)
The slope of the line refers to is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
From the table point A is (5, 18) and B is (12, 16).
The formula of the slope = Δy/ Δx = (y2 – y1)/(x2 – x1)
Hence the slope of line between points A and B is
Slope = (16 – 18)/(12 – 5) = -2/7 = -0.29
Note: The question is incomplete as it is missing options which are A) -0.29 B) -3.5 C) 0.29 D) 3.50 E) -1.00
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Consider the figure shown.
What is the value of q?
A 25°
B 72°
C 108°
D 180°
The value of ∠q is 72 degree. So the option B is correct.
In the given question we have to find the value of q.
The given options are:
A 25 degree
B 72 degree
C 108 degree
D 180 degree
As we know that the angle of straight line is 180 degree.
From the given diagram we can see that the two angel of one line that is cut by another line, is given.
So the third angle of one line that is cut by another line is
25 + 83 + x = 180
x + 108 = 180
Subtract 108 on both side, we get;
x = 72
Using the corresponding angle theorem
∠q = 72 degree
Hence, the value of ∠q is 72 degree. So the option B is correct.
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Find x , y ( 10 points)
Answer:
x = 15
y = 4
Step-by-step explanation:
18/6 = x/5
3/1 = x/5
x = 15
12/y = 3/1
3y = 12
y = 4
Three percent of a man's body is essential fat; for a woman the percentage is closer to 12.5%. As the name implies, essential fat is necessary for a normal healthy body. Fat is stored in small amounts throughout the body. Too much fat, however, can be dangerous to your health. For men between 18 and 39 years old, a healthy percent of body fat ranges from 8% to 19%; for women of the same age, it's 21% to 32%. Measuring body fat can be tedious and expensive. The "standard reference" measurement is by dual-eneregy X-ray absorptiometry (DEXA), which involves two low-dose X-ray generators and takes from 10 to 20 minutes. Because of the time and expense involved with the DEXA method, health professionals would like to be able to make a useable prediction of body fat from easily measurable variables such as weight or waist size.This Excel file shows the waist size (inches), weight (pounds) and percent body fat for 20 individuals. Question 1. What is the slope of the least squares regression line of %body fat on waist size? Correct: Your answer is correct. (use 4 decimal places). Question 2. Find sb1, the estimate of the standard deviation ?b1 of the least squares slope b1 (use 4 decimal places). Correct: Your answer is correct. sb1, estimate of ?b1 Question 3. Determine the 90% confidence interval for the slope of the least squares regression line of %body fat on waist size. Correct: Your answer is correct. lower bound Correct: Your answer is correct. upper bound Question 4. Determine a 90% confidence interval for the mean %body fat found in people with 40-inch waists (use 2 decimal places). lower bound upper bound Question 5. Determine a 90% prediction interval for the %body fat of an individual with a 40-inch waist (use 2 decimal places). lower bound upper bound
Waist (in.) Weight (lb) Body Fat (%)
32 175 6
36 181 21
38 200 15
33 159 6
39 196 22
40 192 31
41 205 32
35 173 21
38 187 25
38 188 30
33 188 10
40 240 20
36 175 22
32 168 9
44 246 38
33 160 10
41 215 27
34 159 12
34 146 10
44 219 28
4) Lower bound = 24.06
Use Dergy Willing
upper bound = 28.55
5)Lower bound = 18.12
upper bound = 34.4
Healthy body=A healthy body is maintained by good nutrition, regular exercise, avoiding harmful habits, making informed and responsible decisions about health, and seeking medical assistance when necessary. Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity .A state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'.
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A pack of gray wolves was reintroduced to a forest. The table gives the size of this population of wolves over time. Which model, in which t represents the time in years, best fits the data in the table?
The exponential equation that represents the population of wolves over time is -
y = 12(1.12)ˣ
What is logarithmic function?The exponential function is a mathematical function denoted by eˣ. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.Inverse : Complex logarithmAt zero : 1Fields of application : Pure and applied mathematicsFixed point : −Wₙ(−1) forMotivation of invention : Analytic proofsIn mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -[tex]y = log_{e}x[/tex]
Given is a table as shown in the question.
Assume the exponential equation to be -
y = A(B)ˣ
At [x] = 0, [y] = 12 -
12 = A(B)⁰
A = 12
and
At [x] = 2, [y] = 15 -
15 = A(B)²
(B)² = 15/12
(B)² = 1.25
(B) = √(1.25)
(B) = 1.118
(B) = 1.12
The equation will be -
y = 12(1.12)ˣ
Therefore, the exponential equation that represents the model is -
y = 12(1.12)ˣ
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Answer:
It's answer B
Step-by-step explanation:
6 Question 5 (5 points) Two masses, m and M. are placed along x-axis at a and b, respectively. Find the center of mass for the system (x, y). 9 (a+b)/2,0 12 0. (a+b)/2 15 O (am+bM)/2,0 (am+bM)/(m+M), O 18 O, (am+bM)/(m+M)
The center of mass for the system (x, y) is [tex]\left(\frac{a m+b M}{m+M}, 0\right)[/tex].
What is center of mass?
The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.
The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.
Centre of mass is
[tex]x=\frac{m a+M b}{m+M}[/tex]
and y=0
[tex](x, y)=\left(\frac{a m+b M}{m+M}, 0\right)[/tex]
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A healthcare provider tested patients experiencing gluten intolerance to determine if they had celiac disease. The relative frequency table summarizes the data.
Tested positive Tested negative Row Totals
Has celiac disease 51% 22% 73%
Does not have celiac disease 14% 13% 27%
Column Totals 65% 35% 100%
What percentage of all patients had a false positive result?
13%
14%
22%
51%
Answer: Option B: 14%
Step-by-step explanation: The only option that seems suitable is option B. You can't have celiac disease and test negative.
Answer:
I think it is 51% or 22%
I am not sure which one, but I think it should be 51% or 22%.
Find f(-1) f(x)=1/3(3)^x
algebra 1
Answer:
1/9
Step-by-step explanation:
f(-1)=1/3(3)^-1
f(-1)=1/3(1/3)
f(-1)=1/9
Rewrite This Integral As An Equivalent Iterated Integral In The Five Other Orders. (Assume Y(X) = Squareroot X And Z(Y) = 8 Y)
The given integral is:
∫ ∫ ( x) ×(8 × (√ x)) dx dy
By changing the order in which we integrate with respect to the variables x and y, we can rewrite this integral as an iterative integral of the other five orders. The other five commands are:
a. ∫ ∫ (√ x) ×(8 × (√t x)) dy dx
b. ∫ ∫ (8 × (√ x)) × (√ x) dx dy
c. ∫ ∫ (8 × (√ x)) × (√ x) dy dx
d. ∫ ∫ (√ x) × (√x) dx (8 × y)
e. ∫ ∫ (√ x) × (√ x) (8 * y) dx
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FILL IN THE BLANK. when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most______model.
when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most data model.
when working on a workbook which requires a team of people to work with you on the workbook, it is important you create transparency and also ensure you complete the workbook on time.
one very important way to complete the task on time is to share the workbook with your team so that they can input their own contributions towards the task, this practice ensures speedy completion of the task. and reduces the level of errors which might have occurred if you where working on it alone.
granting access to the workbook is a very good way to create trust and transparency.
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which of the following scheduling times is needed to obtain the material if it is extrenally produced
Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.
What is scheduling time?Time scheduling is a group of methods for creating and presenting schedules that indicate when work will be done. All of these methods' outcomes are typically displayed as activities or bars on a timeline known as a Gantt chart.
Here,
Obtaining the substance requires the following scheduling if it is externally manufactured.
So ,
When a material is purchased outside, the planned delivery time is the amount of time required to get the material.
Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.
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The complete question is "which of the following scheduling times is needed to obtain the material if it is externally produced or not ?
a.In-house production time.
b.Goods issue processing time.
c. Planned delivery time.
d. Goods receipt processing time."
200 g of water in a glass is at 10.0°C when an ice cube is placed in the glass. What is the temperature of the water after it has transferred 4,200 J of thermal energy to the ice cube? °C
Answer:
20.0°C
Step-by-step explanation:
To find the final temperature of the water after it has transferred thermal energy to the ice cube, we need to use the equation:
Q = cmΔT
where Q is the amount of thermal energy transferred, c is the specific heat capacity of the substance, m is the mass of the substance, and ΔT is the change in temperature.
In this case, we are given that Q = 4,200 J and m = 200 g. The specific heat capacity of water is 4.184 J/g°C.
Substituting these values into the equation gives us:
4,200 J = (4.184 J/g°C)(200 g)(ΔT)
Solving for ΔT gives us:
ΔT = 4,200 J / [(4.184 J/g°C)(200 g)] = 10°C
Since the initial temperature of the water was 10.0°C, the final temperature of the water is 10.0°C + 10°C = 20.0°C.
Therefore, the temperature of the water in the glass is 20.0°C after it has transferred 4,200 J of thermal energy to the ice cube.
A fair die is rolled six times. Calculate the probability of obtaining exactly two 3s. (Round your answer to four decimal places.)
Show work in steps so I can understand how to set up the problem and solve it better. Been stuck on this for awhile! Thanks
The Total Probability of getting exactly two 3s in two throws is 1/36
What is Probability?
A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Solution:
Probability of Obtaining 3 in the first throw = 1/6
Since, the number of possible outcome is 11 and total outcomes are 6
Similarly the probability of getting 3 in the second throw is 1/6
Therefore, total probability = 1/6 * 1/6 = 1/36
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Can someone explain question 2 the perfect square trinmial please please please
The values of m and n required to form perfect square trinomials are given as follows:
a) m = -10, n = 25.
b) m = 6, n = 9.
c) m = 12, n = 180.
d) m = -7/2, n = 49/16.
What are perfect square trinomials?Perfect square trinomials are expressions that have either of these two formats:
(x + y)² = x² + 2xy + y².(x - y)² = x² - 2xy + y².The term that multiplies x is always the multiplication of 2 by both of the two terms that are added.
Hence in item 1, the expression is completed as follows:
x² - 10x = (x - 5)² - 25 = x² - 10x + 25 - 25
Meaning that m = -10, n = 25.
In item 2, the expression is completed as follows:
x² + 6x = (x + 3)² - 9 = x² + 6x + 9 - 9.
Hence m = 6, n = 9.
In item 3, the expression is completed as follows:
5x² + 60x = 5(x² + 12x) = 5(x + 6)² - 180 = 5(x² + 12x + 36) - 180 = 5(x² + 12x + 180 - 180).
Hence m = 12, n = 180.
In item 4, the expression is completed as follows:
2x² - 7x = 2(x² - 7/2x) = 2(x² - 7/4x)² - 49/32 = (2x² - 7/2x + 49/16 - 49/16).
Hence m = -7/2, n = 49/16.
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How do I write an equation for an arithmetic sequence?
The equation for an arithmetic sequence will be;
⇒ T(n) = a + (n - 1) d
Where, 'a' is first term of an arithmetic sequence, 'd' is common difference and 'n' is number of terms.
What is Arithmetic sequence?An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
Given that;
The sequence is an arithmetic sequence.
Now,
Since, The sequence is an arithmetic sequence.
Let 'a' is first term of an arithmetic sequence, 'd' is common difference and 'n' is number of terms.
Then, The nth term of an arithmetic sequence is,
⇒ T(n) = a + (n - 1) d
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suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of per hour. suppose also that a sample culture of bacteria is obtained from this population. find the size of the sample after two hours. round your answer to the nearest integer.
The size of the sample after two hours with an initial population of 1000 and a growth rate of 11% is found to be 1246.
A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth. The formula of continuous exponential growth is P=P₀e^{rt} where P is the population after time t, P₀ is the initial population, and r is the growth rate.
Given P₀ is 1000 bacteria, r is 11% = 0.11, and t is 2 hours. Then, the size of the sample after two hours is,
[tex]\begin{aligned}P&=P_0e^{rt}\\&=1000e^{0.11\times2}\\&=1000e^{0.22}\\&=1000\times1.246\\&=1246\end{aligned}[/tex]
The answer is 1246.
The complete question is -
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 11% per hour. Suppose also that a sample culture of 1000 bacteria is obtained from this population. Find the size of the sample after two hours. Round your answer to the nearest integer.
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the effectiveness of a blood-pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 55.9 for a sample of size 29 and standard deviation 7.4. estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level). assume the data is from a normally distributed population.
We can use the confidence interval formula to estimate how much the drug will lower a typical patient's systolic blood pressure with 80% confidence.
The confidence interval formula is:
Sample mean ± (t-score × standard error)
Where the t-score is calculated from the t-distribution using the number of degrees of freedom (n-1) and the confidence level (80%).
Using the given information, we can calculate the t-score as follows:
t-score = 1.711 (for 80% confidence level and 28 degrees of freedom)
Therefore, the confidence interval is:
55.9 ± (1.711 × (7.4/√29))
= 55.9 ± 4.125
So, with 80% confidence, we can say that the drug will lower a typical patient's systolic blood pressure by between 51.8 and 60.0.
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. if x1, x2, x3 are independent random variables that are uniformly distributed over (0, 1), compute the probability that the largest of the three is greater than the sum of the other two.
The probability that the largest of the three random variables is greater than the sum of the other two is:P(x1 > x2 + x3) = 1/4
The probability of an event occurring is equal to the number of favorable outcomes divided by the total number of outcomes. In this case, the total number of outcomes is 8, since each of the three random variables can take on any value between 0 and 1 independently. The favorable outcomes are those in which x1 is greater than the sum of the other two variables, which is 1/4 of the total number of outcomes. Therefore, the probability that the largest of the three random variables is greater than the sum of the other two is 1/4.
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At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
The test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
To find the mean and standard deviation for the paired differences, prepare the table:
Calculate the value of d bar:
d bar = ∑d/n
= 5+7+...+(-3)/8
= 14/8
= 1.75
Calculate the standard deviation of the (d)
Sd = √(d₁-dbar)²/n-1
= √(5-1.75)²+(7.1-75)²+..+(-3-1.75)²/8-1
= √10.785714
= 3.284
The mean and standard deviation of the eight girls were timed to see how long they could be zero.
Null hypothesis H₀: meand = 0
Alternative hypothesis H₁ : mean d ≠ 0
Level of significance α = 0.05
Decision rule : Reject H₀ when p value < 0.05 level of significance.
The null hypothesis is the 8 girls mean difference between their jumping and relaxed time is equal to the zero and alternative hypothesis is the 8 girls mean difference between their jumping and relaxed time is not equal to the zero.
from the available info, d bar = 1.75 Sd = 3.284
Calculate the test statistic value.
t = 1.75 - 0/3.284/√8
= 1.507
calculate the degree of freedom.
df = n-1
= 8-1
= 7
Calculate the p value of the test
P value = (=TDIST(1.507,7,2)) (use MS Excel function)
= 0.175539
Hence the test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
There is no evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
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Write a function in the form
y = mx + b.
Answer:
y=3/4x-2
Step-by-step explanation:
Students pay $2 per ticket and adults pay $5 per ticket. Although the stadium is filled to its capacity of
2000, 254 of those seats are given free of charge to band members, pep squad members, and faculty members. the ticket-booth manager reports to the athletic director that the total income from the sale of tickets for the current game is $5766. How many student and adult tickets were sold?
The number of students and adult ticket sold are 988 and 758 respectively .
How to find the number of student and adult tickets?Students pay $2 per ticket and adults pay $5 per ticket. The stadium is filled to its capacity of 2000 but 254 of those seats are given free of charge to band members, pep squad members, and faculty members.
The total income from the sale of tickets for the current game is $5766.
The number of student and adult tickets that were sold can be calculated as follows:
let
x = number of student ticket sold
y = number of adult ticket sold
Hence, using equation,
Students pay $2 per ticket and adults pay $5 per ticket and the total total sale is 5766.
2x + 5y = 5766
The stadium is filled to its capacity of 2000 but 254 of those seats are given free. This means the actual number of people that paid for the seats is 2000 - 254 = 1746.
x + y = 2000 - 254
x + y = 1746
Combine the equation
2x + 5y = 5766
x + y = 1746
multiply equation(ii) by 2
2x + 5y = 5766
2x + 2y = 3492
subtract equation(ii) from equation(i)
3y = 2274
y = 2274 / 3
y = 758
x = 1746 - 758
x = 988
Therefore,
number of student tickets = 988
number of adult tickets = 758
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