Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.281 = 28.1% probability that the sample mean is above 500.
b) 0.0003 = 0.03% probability that the sample mean is above 500.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 430, hence [tex]\mu = 430[/tex].The standard deviation is of 120, hence [tex]\sigma = 120[/tex].Item a:
The probability is the p-value of Z when X = 500, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 430}{120}[/tex]
[tex]Z = 0.58[/tex]
[tex]Z = 0.58[/tex] has a p-value of 0.719.
1 - 0.719 = 0.281
0.281 = 28.1% probability that the sample mean is above 500.
Item b:
Sample of 35, hence [tex]n = 35, s = \frac{120}{\sqrt{35}}[/tex]
Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{500 - 430}{\frac{120}{\sqrt{35}}}[/tex]
[tex]Z = 3.45[/tex]
[tex]Z = 3.45[/tex] has a p-value of 0.9997.
1 - 0.9997 = 0.0003
0.0003 = 0.03% probability that the sample mean is above 500.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
What’s a rational number between -1/6 and 1/9
Answer:
LCM of 6 and 9 are 18
1/6 = 1×3/6×3
= 3/18
= 3×10/18×10
= 30/180
1/9 = 1×2/9×2
= 2/18
=2×10/18×10
= 20/180
therefore rational no.s between 1/6 & 1/9 are
21/180,22/180,23/180,24/180,25/180,26/180,27/180,28/180,29/180
Step-by-step explanation:
sorry if im wrong
Answer:
1/18.
Step-by-step explanation:
-1/6 = -3/18 and 1/9 = 2/18
so one rational number between these values is 1/18.
Over the course of 12 hours the temperature changes a tour of -16°C what is the average change in temperature in one hour
Answer:
- 1 1/3 degree
Step-by-step explanation:
- 16 / 12
What is Jada‘s vertical jump
It's probably 52 or 40.
#10) Mrs. Sommer states that angle I is 65 degrees. Is she correct? why or why not
Answer: Mrs. Somner is correct.
Step-by-step explanation: In a triangle, the angles add up to 180 degrees. Since we know that Triangle ABC is equal to Triangle RST, we can assume that their angle values are equal as well. Angle A is 41 degrees, and Angle B is 74 degrees. This adds up to 115 degrees. If we subtract 115 from 180, we get 65. Therefore, Mrs. Somner is correct.
The table shows a linear relationship between x and y. how can you tell that x and y are NOT porportianal
Help with number 2
No links
No jokes to just get points
Answer:
A. Circle -2.5x and 1.7x list x B. List t and s C. Circle 15k and 2/5k list k and m
Step-by-step explanation:
You do it??
A line with a slope of 3 passes through the point (0, -10). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{3}(x-\stackrel{x_1}{0}) \\\\\\ y+10=3x\implies \stackrel{\textit{slope-intercept form}}{y=3x-10}[/tex]
Find the area of the figure. hi
We figure 25 people will attend if it rains and 70 people will attend if it does not rain. The weather forecast indicates that there is a 20% chance of rain that day. What is the expected number of people who will attend the party?
Answer:
34
Step-by-step explanation:
20% of 70 + 80% of 25 = 14 + 20 = 34.
Answer:
61
Step-by-step explanation:
Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).
The expected number of people with a 20% chance of rain would be 61.
(hope it helps)
50 POINTS
What is the slope-intercept form of the linear equation 2x + 3y = 6? Drag and drop the appropriate number, symbol, or variable to each box.
Isaac bought 7 chicken wings for $12.60. How much does each wing cost?
Answer:
Each chicken wing costs $1.80.
Explanation:
To find the cost for each wings, you need to split the money by 7 which is: 12.60/ 7
this gives us:
1.80
Choose the symbol that correctly compares the fractions below.
Answer:
[tex] \frac{2}{5} > \frac{1}{6} [/tex]
Answer: B. >
#CarryOnLearning
The polygons are similar. The area of one polygon is given. Find the area of the other polygon.
Answer:
108 ft²
Step-by-step explanation:
For the polygon on the left, we are given the length of one side (3 ft) and the total area (27 ft²). With this information, we can determine the length of the other side - 9 ft. I found this by dividing 27 ft² by 3 ft, giving me the final result of 9 ft.
Next, we have to find the other side of the polygon on the right so we can ultimately determine its area. It looks like there is a scale factor of 2 between the two polygons, since 3 × 2 = 6. We know that the bottom side of the left polygon is 9, so multiplying 9 by 2 should give us the bottom side of the polygon on the right. 9 × 2 = 18.
Now, we have the side lengths for the polygon on the right and can determine its area. What is 6 ft × 18 ft? Well, the answer is 107 ft², and this is the answer to the question.
Hopefully that's helpful! :)
find the value of 7u+7 given that -3u-5=4
(a) The perimeter of a rectangular garden is 320 m.
If the width of the garden is 74 m, what is its length?
(b) The area of a rectangular window is 5723 cm?
If the length of the window is 97 cm, what is its width?
Width of the window: cm what is the width
Answer:
86 m, 59 cm
Step-by-step explanation:
a. perimeter is 2L + 2W
320 = 2L + 2(74)
320 = 2L + 148
172 = 2L
86 m is length
b. area = L x w
5723 = 97 x w
5723/97 = 2
59 cm is width
SOMEONE PLEASE HELP QUICKLY
A commercial claims that 8 out of 10 dentists recommend a certain brand of toothpaste. To test this claim, a random sample of 85 dentists is obtained. Of these 85 dentists, 73 indicated that they recommend that brand of toothpaste. Using a significance level of 5%, test the claim to see if the proportion of dentists who recommend this toothpaste is not 8 of 10.
a) State the null and alternative hypotheses
b) State the p value
c) Make a conclusion about the claim
Answer:
rgb
Step-by-step explanation:
wrtbtrb
a) The null hypothesis is: p = 0.8 and the alternative hypothesis is p ≠ 0.8.
b) p-value is 0.0838
c) We accept the null hypothesis
What are null and alternative hypothesis?The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
What is p-value?A p-value is a statistical measurement used to validate a hypothesis against observed data.
a. Let p be the proportion of 8 out of 10 dentists.
The null hypothesis is
[tex]H_0 : p=\frac{8}{10}=0.8[/tex]
The alternative hypothesis is
[tex]H_1:p\neq 0.8[/tex]
b. The sample proportion [tex]\hat p=\frac{73}{85}\approx 0.86\\[/tex]
Z-score, the test statistic is
[tex]Z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}}{n} } \\\\Z=\frac{0.86-0.8}{\frac{\sqrt{0.8(1-0.8)}}{85} }\\ \\Z=\frac{0.06}{0.043386}\\ \\Z=1.3829\\\\Z\approx 1.38[/tex]
P(Z > 1.38) = 1 - P(Z < 1.38)
∴ P(Z > 1.38) = 1 - 0.9162 = 0.0838
p-value is 0.0838
c. Since the p-value is greater than the level of significance α=0.05, we reject the alternative hypothesis and accept the null hypothesis
For more information on null hypothesis: https://brainly.com/question/19263925
#SPJ2
answer both pls help fast
Answer:
Answers given in the photo
f(x)=5x+4, g(x) square root of x find the domain of gof
A B C or D? please help
Answer:
(x-1) and (x-5)
Step-by-step explanation:
option a .......
What is 5+5 ..................................................
Answer:
10
Step-by-step explanation:
5+5=10
each hand has five fingers so if you count all of the fingers on both hands, you will get 10
line of best fit gina wilson. It says stuff about Hannah as a baby and her weight. plz help
PLLLZZZ NO ONE WILL HELP ME!!!
Given this equation in slope-intercept form…
y = 2x + 5
Identify or solve for the following:
Slope
y-intercept
x-intercept
Independent variable
Dependent variable
Domain
Range
We would like to represent a line passing through the point (5,0) with a slope of 2. Please write the equation for this line in slope-intercept form and in point-slope form.
What is the rate of change of the function above?
Answer:
y = m x + b standard form of straight line
y = 2 x + 5
The slope is m and = 2
the y intercept is 5 because when x = o y = 5
if y = 0 then x = -2/5 and would be the x intercept
x is the independent variable and y is the dependent variable
I am not familiar with your definitions for domain and range but
both x and y can vary from -∝ to = ∝
Help me please I would really apparated it thanks.
Joshua cashed a check for $16.79he asked the teller to give him as many quarters as possible .how many quarters did he get
Answer:
67 quarters
Explanation:
Luis wants to but a skateboard that usually sell for $79.64. All merchandise is discounted by 12%
Answer:
$79.64
Step-by-step explanation:
I think it's still 79.64
Answer:
it will be equal 70.08 $
Determine the slope from the given graph below:
The slope is 4
The slope is -4
The slope is−14
The slope is -2
Answer:
-4
Step-by-step explanation:
rise over run
rise being y axis
run being x axis
in this case y intercept is 4 and x intercept is1
Solve each inequality 3+1/2(3-x)<_7
Answer:
x > 5
Step-by-step explanation:
multiply the fractions, break up the fraction, group like terms, convert integer into a fraction, combine the fraction, combine the numerator, etc. hope this helps.
Riley is saving up to buy a new television. She needs a total of $966.42. Riley has saved $200.92 already and earns $76.55 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television
Answer:
10 weeks
Step-by-step explanation:
76.55x+200.92=966.42
76.55x=966.42-200.92
76.55x=765.5
x=765.5/76.55
10
which statement best describes the first step to the equation -11-3x=44-2x
A. add 3 to both sides
B add 2 to both sides
C.get the variables on one side
Get the variables on one side statement best describes the first step to the equation -11-3x=44-2x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -11-3x=44-2x
Minus eleven minus three x equal to forty four minus two times of x
To solve this, we need to seperated the variable on one side
-3x+2x=44+11
-x=55
x=-55
Get the variables on one side is the first step to the equation -11-3x=44-2x
Hence, get the variables on one side statement best describes the first step to the equation -11-3x=44-2x
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ5
I will mark as brainliest if answer is correct.
Which ordered pair is a solution to the system of inequalities?
y≥2x-1
y<4x
A. (2,6)
B. (3,2)
C. (3,4)
D. (2,8)