Assume that the distributions for the following scenarios are normal. Use the normal standard table to find the following probabilities. Round z-scores to the nearest hundredth.
1. The average score on a math test is 75 with a standard deviation of 8. What is the probability that a randomly selected test has a score of 90 or higher?
2. The life of a gas grill is 3.5 years with a standard deviation 0.35 years. What is the probability that the grill will last less than 3 years?
3. Ambulance response times average 7.5 minutes with a standard deviation of 2.5. What is the probability that an ambulance will respond within 6 to 8 minutes.
Answers
Answer:
1. To find the probability that a randomly selected test has a score of 90 or higher, we need to find the z-score corresponding to a score of 90 and then use the standard normal table to find the probability that a score is greater than or equal to this value. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the score we are interested in, mean is the average score, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z = (90 - 75) / 8 = 1.875
Rounding this value to the nearest hundredth, we get z = 1.88. Looking up this value in the standard normal table, we find that the probability that a score is greater than or equal to 1.88 is 0.9637. Therefore, the probability that a randomly selected test has a score of 90 or higher is 0.9637.
2. To find the probability that the grill will last less than 3 years, we need to find the z-score corresponding to a life of 3 years and then use the standard normal table to find the probability that a life is less than this value. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z = (3 - 3.5) / 0.35 = -1.43
Rounding this value to the nearest hundredth, we get z = -1.43. Looking up this value in the standard normal table, we find that the probability that a life is less than -1.43 is 0.0747. Therefore, the probability that the grill will last less than 3 years is 0.0747.
3. To find the probability that the ambulance will respond within 6 to 8 minutes, we need to find the z-scores corresponding to a response time of 6 and 8 minutes, respectively, and then use the standard normal table to find the probability that a response time is between these two values. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z1 = (6 - 7.5) / 2.5 = -0.6
z2 = (8 - 7.5) / 2.5 = 0.2
Rounding these values to the nearest hundredth, we get z1 = -0.6 and z2 = 0.2. Looking up these values in the standard normal table, we find that the probability that a response time is less than -0.6 is 0.2743 and the probability that a response time is less than 0.2 is 0.5398. Therefore, the probability that a response time is between -0.6 and 0.2 is 0.5398 - 0.2743 = 0.2655. Therefore, the probability that the ambulance will respond within 6 to 8 minutes is 0.2655.
1. The probability that a randomly selected test has a score of 90 or higher is 0.0301.
2. The probability that the grill will last less than 3 years is 0.0764.
3. The probability that an ambulance will respond within 6 to 8 minutes is 0.1465.
How to determine the required probabilities?In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Part 1.
By substituting the given parameters, we have the following:
Z-score, z = (90 - 75)/8
Z-score, z = 1.88
Based on the standardized normal distribution table, the required probability is given by:
P(Z ≥ 1.88) = 1 - P(x < Z)
P(Z ≥ 1.88) = 1 - 0.9699
Probability = 0.0301.
Part 2.
By substituting the given parameters, we have the following:
Z-score, z = (3 - 3.5)/0.35
Z-score, z = -1.43
Based on the standardized normal distribution table, the required probability is given by:
P(Z < -1.43) = 1 - P(x > Z)
P(Z < -1.43) = 1 - 0.9236
Probability = 0.0764.
Part 3.
At 6 minutes, we have:
Z-score, z = (6 - 7.5)/2.5
Z-score, z = -0.6
At 8 minutes, we have:
Z-score, z = (8 - 7.5)/2.5
Z-score, z = 0.2
Based on the standardized normal distribution table, the required probability is given by:
P(6 < x < 8) = P(-0.6 < z < 0.2)
P(-0.6 < z < 0.2) = P(z < 0.2) - P(z < -0.6)
P(-0.6 < z < 0.2) = 0.42074 - 0.27425
P(-0.6 < z < 0.2) = 0.1465.
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Related Questions
Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?
A
2/36
B
3/36
C
3/15
D
2/9
E
4/6
Answers
Answer:
e
Step-by-step explanation:
because it's number is common
The probability generating function of the dis- crete nonnegative integer valued random variable X having probability mass function pj, j = 0, is defined by ø(s) = E[s] =Σp;si j=0 Let Y be a geometric random variable with param- eter p 1 s, where 0 < s < 1. Suppose that Y is independent of X, and show that ø(s) = P{XY}
Answers
The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}
In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.
First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.
We can now substitute this expression into the probability generating function for X. We have that ø(s)
= E[s] = Σp;si j=0
= Σ pi pj sij
= P{XY}
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with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
Answers
Answer:
sorry new don't understand the app
you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
Answers
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
What is Confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Given 131 population
Standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
Determine the upper control limit if desired confidence interval is 99.73%
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]
Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
Value of z* for 99.73% confidence interval is 3.00.
So margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
If we want a confidence level of 99.73%, the top control limit is 16.4.
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Question
Newton's Law of Universal Gravitation: The gravitation attraction, f , between two objects of masses x and y is proportional to the product of the masses and inversely proportional to the square of the distance, d , between the objects.
Write an equation for the constant of variation, k, in terms of f, x, y, and d.
Complete the equation in the space below (do not enter “k=“)
Answers
The required equation for the variation of k is given as k = Fd² / xy.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,
F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)
Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²
Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy
Thus, the required equation for the variation of k is given as k = Fd² / xy.
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write an equation of the line that passes through the given point and is parallel to the given line. (see example 2.) 7. (0, 2); x
Answers
Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
According to our question-
Given line: 2x+5y−7=0
the mid - point of the line segment joining point (2,7) and (−4,1) is
( 2(2−4 )2(7+1))=(−1,4)
the equation of the line will be
y−y 1=m(x−x 1)y−4=( 5−2 )(x+1)
5y−20=−2x−2
2x+5y=18
Hence, Equation of the line parallel to the given line and passing through the given point = 2x+5y=18.
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two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .
Answers
The two events a and b are independent if and only if (a) Events a and b are independent .
What are Independent Events ?
Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .
The probability of two independent events can be mathematically represented as P(A and B) = P(A) × P(B) .
So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Two events, a and b are independent if and only if
Which of the following statements is true of a and b?
(a) Events a and b are independent
(b) Events a and b are not independent, but they are mutually exclusive
(c) Events a and b are not independent since and .
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For which equation would x = 12 be a solution?
Ox+4≤12
12 x < 200
012-x24
O 12÷x>12
Answers
Answer:
the second solution would be correct 12x < 200
Step-by-step explanation:
12x < 200
12(12) <200
144 < 200
A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.
a) If an employee tests positive for drug use, what is the probability that they actually use drugs?
b) What is the probability that a nondrug user will test positive for drug use twice in a row?
c) What is the probability that someone who tests positive twice in a row is not a drug user?
Answers
a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%
b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user is 23%
What is Bayes' theorem in probability?Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.
The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.
The question state that
Pr(D) = 0.10
Pr(D') = 0.90
Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)
Pr(P/D') = 0.05
a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')
⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)
⇒ Pr(D/P) = 0.098/(0.098+0.045)
⇒ Pr(D/P) = 0.098/0.143
⇒ Pr(D/P) ≈ 0.6853
⇒ Pr(D/P) ≈ 69%
b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')
⇒ Pr (P*2/D') = 0.05*0.05
⇒ Pr (P*2/D') = 0.0025
⇒ Pr (P*2/D') = 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)
⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)
⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604
⇒ Pr (D'/P*2) = 0.00225/0.09829
⇒ Pr (D'/P*2) ≈ 0.2289
⇒ Pr (D'/P*2) ≈ 23%
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let $d$ be any positive integer not equal to $2, 5$ or $13$. show that one can find distinct $a,b$ in the set $\{2,5,13,d\}$ such that $ab-1$ is not a perfect square.
Answers
The statement given in the question holds true . We get this result after analyzing the given data set .
Given , hypothesis is ,
Let d be any positive integer not equal to2 , 5 or 13 .
Show that one can find distinct a , b in the set {2,5,13,d} such that ab-1 is not a perfect square.
Using the modular way to solve this question we get ,
d = 0 , 3 = | 4 |
Then , we get the result as ,
13d - 1 , which is not a perfect square.
d = 2|4|
we get , 2d -1
which again is not a perfect square.
Similarly after checking the value for all the possible cases , we will get the result that the hypothesis is correct.
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scenario 2: an analyst wants to know if the proportion of smokers in the population is the same in usa and canada. in order to test this hypothesis she collects data from individuals, both smokers and non-smokers, living in these countries. your task is to help the analyst perform her hypothesis test. in order to do this you need to compute various statistics using excel. use 5% level of significance. [scenario 2: q1] the proportion of smokers in the us sample is . 0.17 0.06 0.16 0.12 0.40
Answers
The conclusion statement of the hypothesis is to reject the null hypothesis and accept the alternative hypothesis and the z score of -121.70 is in the rejection area
How to calculate the hypothesis?
In order to calculate, the hypothesis test we have to make inferences about the population data. It is also used to check if the results of an experiment are valid.
Here we have given that an analyst wants to know if the proportion of smokers in the population is the same in USA and Canada. in order to test this hypothesis she collects data from individuals, both smokers and non-smokers, living in these countries. your task is to help the analyst perform her hypothesis test. in order to do this you need to compute various statistics using excel. use 5% level of significance.
Here we have the following sample of data,
0.17 0.06 0.16 0.12 0.40
Through the given samples, we have identified the following values,
Count, N: 5
Sum, Σx: 0.91
Mean, μ: 0.182
Variance, σ2: 0.013376
Then the hypothesis test is written as,
The critical value (cutoff point) is 2.132. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since -121.70 is less than 2.132, we reject the null hypothesis. We accept the alternative hypothesis.
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maya spent a total of 80% at the grocery store. of this amount, she spent $44 on fruit. what percentage of total did she spend on fruit
Answers
The percentage of total that Maya spend on fruit is 55%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. The percentage of total that she spend on fruit will be:
= Amount on fruit / Total amount × 100
= 44/80 × 100
= 55%
The percentage is 55%.
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Complete question
maya spent a total of $80 at the grocery store. of this amount, she spent $44 on fruit. what percentage of total did she spend on fruit
In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares?
Multiple Choice
1.07
0.17
0.320
8.74
Answers
In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.35 and SSR = 4.18. What is the error sum of squares is 0.17.
What do you meant by squares?A square is a figure with four equal sides and four right angles. It's a popular shape for windows and record albums, among many other things.Square has many different metaphorical uses. Old towns had square open areas for meetings, so now "town square" means meeting place, even if it's not shaped exactly like a square. If you settle your debts, you square them, and if someone calls you a square, they mean you're boring, rule-abiding, and lame. In math, a square is the product of something multiplied by itself. If you square your plans with someone, you line them up.To learn more about square refer to:
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Select all of the equations for the line that passes through (5, −2) and (0, 18).
Multiple select question.
A)
y+2=−4(x−5)
B)
x+4y=−12
C)
y−6=−4(x+1)
D)
y=−4x−12
E)
y=−4x+18
F)
4x+y=18
Answers
Answer:
Need more info please
Step-by-step explanation:
Select the correct answer. When using the binomial formula, which of the following is a correct step in the expansion of (x + y)? 4(4-1)(4-2) (4-³)³ + 31 24 + 24 + 24 + ○ D. x + Ο Α. OB. C. x(4-¹)y + 4(4-¹) (4-2) y² + 2(4-¹)y + 4(4-¹) x(4-2) y² + x(4-1)y + 4(4-¹)(4-2)² + (4-1)(4-2)(4-3)3 + 4(4-1)(4-2)(4-3) (4-4) z 4(4 − 1)(4 − 2)(4 — 3) (4-4) - 3 4(4-1)(4-2) (4-3)³ + 3 4(4-1)(4-2)(4-3) (4-4) 41 4(4 − 1)(4 − 2)(4 — 3) (4-4) (4-1)y + 4(4-1)(4-2) (4-3)³ +
Answers
Jaquan bought an RV for $95,000. He made a down payment of $72,000 and paid $650 monthly for 60 months. What's the total finance charge?
Answers
If Ethan has $40, what's the most amount of games he could bowl at Happy Bowl (after he rented shoes)?
Answers
Answer:
he could play 4 games and have some change left over
Step-by-step explanation:
renting shoes cost 5 dollars and each game costs 8 dollars so 40-5=35 35/8=4.375
Armando divided 6 and 258
Answers
Answer:
43
Step-by-step explanation:
258 divided by 6 equals 43
Look below
Armando divided 6 and 258
258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:
258÷6
then just put it on a calculator and you get the answer 43. hope that helps
Liam accidentally charged more on his debit card than he had in his checking account. His balance is now -$12.75. He is charged a $10 overdraft fee each day his account balance is below $0. He makes no other withdrawals or deposits. Which equation accurately represents his balance, y, after x days?
Answers
Answer:
The equation that accurately represents Liam's balance, y, after x days is y = -12.75 - 10x.
This equation takes into account the fact that Liam's balance is already -$12.75 and that he is charged a $10 overdraft fee each day his balance is below $0. As the number of days, x, increases, the total amount of overdraft fees he is charged will also increase, resulting in a decrease in his balance.
For example, if Liam's balance is -$12.75 after 0 days, his balance will be -$22.75 after 1 day (y = -12.75 - 10(1) = -22.75), and his balance will be -$32.75 after 2 days (y = -12.75 - 10(2) = -32.75).
Round the answer to the nearest tenth please
Answers
Answer:
19.9 m
Step-by-step explanation:
Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)
1/3 x π x 1^2 × 2 = 2.0943951023932
2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)
Cylinder: r= 1m Height= 5m
π x 1^2 x 5 = 5π = 15.707963267949
Now add both together then round to tenths.
4.1887902047864 + 15.707963267949 = 19.8967534727354
(Remember use hundreths place if writing down)
19.8967534727354 --> 19.9 m
In evaluating a double integral over a region D. a sum of iterated integrals was obtained as follows: Sketch the region D and express the double integral as an iterated integral with reversed order of integration.
Answers
Let D be the region bounded by the lines y = 0, y = x, x = 1, and x = 2. In order to express the double integral as an iterated integral with reversed order of integration, we first need to sketch the region D.
The double integral could be expressed as an iterated integral with reversed order of integration as follows:
[tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex]
The region is bounded by the lines y = 0, y = x, x = 1, and x = 2. This forms a triangle-like shape with 1 and 2 being the x-coordinates of the vertices and y = 0 being the base of the triangle. Then, we can express the double integral as: [tex]$\int_{1}^{2}\int_{0}^{x}f(x,y)dydx$[/tex], where the order of integration is reversed from the original double integral. This means that first we are integrating with respect to y from 0 to x, and then we are integrating with respect to x from 1 to 2.
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Which of the following represents a nonlinear function?
y=x²
y=x
y=-2 x
y=5 x+7
Answers
The equation that represents a non linear function is y = x² , the correct option is (a) .
In the question ,
four functions are given ,
we have to select the option that is non linear ,
we know that ;
A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line . and
A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .
So , from the given options
we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .
Therefore , The Non Linear Function is (a) y = x² .
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a current i(t) with arbitrary time dependence is around a circular ring. derive the general formula for the power radiated,
Answers
P = ∫(i^2 dl / 6πε0 c^3) × a^2
where q is the charge, ε0 is the permittivity of free space, c is the speed of light, and a is the acceleration of the charge.
Now consider a small element of length dl around the ring through which the current i flows. The power radiated from this element can be written as
dP = (i^2 dl / 6πε0 c^3) × a^2
where a is the acceleration of the charge in the element due to the changing magnetic field.
The total power radiated from the entire ring is obtained by integrating this expression over the length of the ring.
P = ∫(i^2 dl / 6πε0 c^3) × a^2
This is the general expression for the radiated power of the current distribution around the ring.
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Last year, Alan opened an investment account with $7200. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of the year?
Answers
Answer:
1) $468
2) 7668
Step-by-step explanation:
1) 6.5% of 7200 is 468. Therefore, this is the amount it had increased.
2) 7200+468=7668 Total for the end of the year
Your company creates haircare and skincare products in large quantities. You have a cylindrical storage tank that’s going to be used for a new batch of shampoo. The tank is 170 feet across in diameter and 60 feet high.
Use this formula sheet for your calculations.
Part A
To calculate the volume of this cylindrical tank, what preliminary calculations must be done with the information given in the problem?
Answers
To calculate the volume of a cylindrical tank, you will need to use the formula for the volume of a cylinder, which is:
V = πr^2h
Where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
To use this formula, you will need to first calculate the radius of the base of the tank. To do this, you will need to divide the diameter of the tank (170 feet) by 2.
Once you have calculated the radius, you can plug the value into the formula along with the height of the tank (60 feet) to find the volume of the tank.
Answer:
Step-by-step explanation:
height of the tank= 60 feet
diameter = 170 feet.
as we know, radius = 2 *diameter
therefore radius = diameter /2
= 170/2
=85 feet
volume of cylinder = πr²h
π =3.14
= 3.14 ×85×60
=10927.2 feet²
A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unac- ceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.016 mm. (a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm? Calculate a P-value to draw conclusions. State any necessary assumptions about the underlying distribution of the data. (b) Construct a 95% lower confidence bound for o. (c) Use the confidence bound in part (b) to test the hypothesis.
Answers
Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
Given that;
H₀ : σ = 0.02
H₁ : σ > 0.02
The test statistics is;
X² = ( n-1 )s² / σ² = ( 15 - 1)(0.016)² / (0.02)²
= 0.003584 / 0.0004
= 8.96
degree of freedom
df = n - 1 = 15 - 1 = 14
For right tailed test, critical value at 0.01 level of significance is 29.141.
Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),
Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
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PLEASE HELP ASAP!!!
A machine at a bakery poured out flour for 16 minutes. At the end of that time, the machine was empty. The graph shows the amount of flour (in grams) remaining in the machine versus time (in minutes). Find the range and the domain of the function shown.
Answers
Answer:
R = 0≤ y ≤ 800
D = 0≤ x ≤ 16
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Hello can someone please help me find x. Im getting stuck. Thanks!
Answers
The value of the x is 3.26556.
What is the Intersecting Chord Theorem?
When two chords intersect each other inside a circle, the products of their segments are equal.
We have,
It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.
One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).
According to Intersecting Chord Theorem:
This theorem states that A×B is always equal to C×D no matter where the chords are.
A.B = C.D
(x+10) * (x+1) = (x) * (5x+1).
x² + x + 10x + 10 = 5x² + x
x² + x + 10x + 10 - 5x² - x = 0
-4x² + 10x + 10 = 0
using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get
x=−0.765564
x = 3.26556
Hence, the value of the x is 3.26556.
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what is the area of this triangle
30POINTS
Answers
Answer:
81.74 cm²
Step-by-step explanation:
Use tan(x) to find x
tanθ = opposite/adjacent
tan(36) = x/15
15tan(36) = x
area of triangle = [tex]\frac{1}{2}[/tex]*b*h
[tex]\frac{1}{2}[/tex]*15tan(36)*15 = 81.74 cm² (2 d.p.)
please help me answer this math question
Answers
Answer:
k>0: ]-∞, 1[ v ]9 , +∞[
Step-by-step explanation:
we know that D > 0 because the anwser has to have two outcomes so:
b²-4.a.c>0 => (k-3)²-4.k.1>0 <=> k²-6k+9-4k>0 <=> k²-10k+9>0
=> D=8² : x1 = 9 v x2 = 1
k>0: ]-∞, 1[ v ]9 , +∞[