Question 1

A normal quartile plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

Accepted Answer

Since the normal quartile plot...

Question 2

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

Accepted Answer

A)   The area between 43.5 and 45.5
B)   The area between 43.5 and 44
C)   The area between 43.5 and 44.5
D)   The area between 44 and 44.5E) A) and C)
F) A) and B)

Question 3

If  z  is a standard normal variable, find   0.97 ) ">P(z>0.97) P ( z > 0.97 ) P(z>0.97)

Accepted Answer

A)    0.1922 
B)    0.1660 
C)    0.8340 
D)    0.1685  E) B) and C)
F) A) and D)

Question 4

Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 5, 7, and 9. Consider the
values of 5, 7, and 9 to be a population. Assume that samples of size n = 2 are randomly
selected with replacement from the population of 5, 7, and 9. The nine different samples are
as follows: (5, 5), (5, 7), (5, 9), (7, 5), (7, 7), (7, 9), (9, 5), (9, 7), and (9, 9). (i)Find the mean
of each of the nine samples, then summarize the sampling distribution of the means in the
format of a table representing the probability distribution. (ii)Compare the population mean
to the mean of the sample means. (iii)Do the sample means target the value of the
population mean? In general, do means make good estimators of population means? Why or
why not?

Accepted Answer

(i)
people.
(iii) The sample means tar...

Question 5

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate  P(6)   for  n=18  and  p=0.3 .

Accepted Answer

A)    0.1239 
B)    0.1015 
C)    0.8513 
D)    0.1958 E) A) and B)
F) C) and D)

Question 6

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population
that is not normally distributed

Accepted Answer

The central limit theorem: for all samples of the same size $n$ with $n > 30$, the sampling distribution of $\bar { x }$ can be approximately by a normal distribution with mean $\mu$ and standard deviation $\sigma / \sqrt { n }$. If an original population is not normally distributed, the distribution is approximately a normal distribution if $n > 30$.

Question 7

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6. What are the values of the mean and standard deviation after all test scores have been standardized by converting them to z-scores using zx=−() μ /σ?

Accepted Answer

A)   The mean is 100 and the standard deviation is 10.
B)   The mean is 0 and the standard deviation is 1.
C)   The mean is 10 and the standard deviation is 100.
D)   The mean is 1 and the standard deviation is 0.E) A) and B)
F) None of the above

Question 8

Using the following uniform density curve, answer the question.

What is the probability that the random variable has a value greater than 5 ?

Accepted Answer

A)    0.325 
B)    0.250 
C)    0.375 
D)    0.500 E) B) and C)
F) B) and D)

Question 9

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Accepted Answer

Assume that the random variable <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> has a d...

Question 10

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

Accepted Answer

A)   0.4332
B)   0.9332
C)   0.0668
D)   0.5E) A) and B)
F) B) and D)

Question 11

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what pattern would you expect in a normal quantile plot of these data?

Accepted Answer

A)   The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern.
B)   The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be bell-shaped.
C)   The histogram would by non-symmetric, and the normal quantile plot would have data points that would be non-linear.
D)   The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be non-linear.E) B) and C)
F) C) and D)

Question 12

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

Accepted Answer

A)   0.1554
B)   0.3811
C)   0.2257
D)   0.0703E) A) and B)
F) All of the above

Question 13

If  z  is a standard normal variable, find the probability:  P(−0.73<z<2.27) P ( - 0.73 < z < 2.27 ) P(−0.73<z<2.27)

Accepted Answer

A)    0.7557 
B)    1.54 
C)    0.4884 
D)    0.2211  E) All of the above
F) C) and D) A

Question 14

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

Accepted Answer

A)   0.5080
B)   0.4910
C)   0.0948
D)   0.4920E) C) and D)
F) None of the above B

Question 15

In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is
Between 1100 kWh and 1225 kWh.

Accepted Answer

A)   0.3791
B)   0.2881
C)   0.1971
D)   0.0910E) A) and D)
F) A) and C)

Question 16

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of no more than 35 defective CDs

Accepted Answer

A)   The area to the left of 35
B)   The area to the left of 35.5
C)   The area to the right of 35.5
D)   The area to the left of 34.5E) C) and D)
F) B) and D)

Question 17

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

Accepted Answer

A density curve is a graph of a continuo...

Question 18

Assume that  z  scores are normally distributed with a mean of 0 and a standard deviation of  1. If  P(−a<z<a) P ( - a < z < a ) P(−a<z<a)    =0.4314 , find  a.a .a.

Accepted Answer

A)    -0.18 
B)    0.3328 
C)    0.57 
D)    1.49  E) A) and B)
F) B) and C)

Question 19

Scores on a test have a mean of 70 and   Q3Q _ { 3 }Q3​  is 83 . The scores have a distribution that is approximately normal. Find  P90P _ { 90 }P90​  (You will need to first find the standard deviation.)

Accepted Answer

A)    92.9 
B)    93.7 
C)    95.6 
D)    94.8  E) A) and B)
F) B) and D)

Question 20

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Find the value closest to the probability that a randomly selected woman has a red
Blood cell count above the normal range of 4.2 to 5.4 million cells per microliter.

Accepted Answer

A)   0.1611
B)   0.0409
C)   0.0158
D)   0.9842E) B) and D)
F) A) and C)

Exam 6: Normal Probability Distributions

A normal quartile plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

Correct Answer
verified
Since the normal quartile plot...
View Answer

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

Correct Answer
verified

If z is a standard normal variable, find $P ( z > 0.97 )$

Correct Answer
verified

Correct Answer
verified
(i)
people.
(iii) The sample means tar...
View Answer

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate P(6) for n=18 and p=0.3 .

Correct Answer
verified

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distributed

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6. What are the values of the mean and standard deviation after all test scores have been standardized by converting them to z-scores using zx=−() μ /σ?

Correct Answer
verified

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5 ?

Correct Answer
verified

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Correct Answer
verified
Assume that the random variable has a d...
View Answer

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

Correct Answer
verified

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what pattern would you expect in a normal quantile plot of these data?

Correct Answer
verified

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

Correct Answer
verified

If z is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27 )$

Correct Answer
verified
A

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

Correct Answer
verified
B

Correct Answer
verified

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of no more than 35 defective CDs

Correct Answer
verified

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

Correct Answer
verified
A density curve is a graph of a continuo...
View Answer

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $P ( - a < z < a )$ =0.4314 , find $a .$

Correct Answer
verified

Scores on a test have a mean of 70 and $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ (You will need to first find the standard deviation.)

Correct Answer
verified

Correct Answer
verified

Exam 6: Normal Probability Distributions

A normal quartile plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

Correct AnswerverifiedSince the normal quartile plot...View AnswerShow Answer

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

Correct AnswerverifiedShow Answer

If z is a standard normal variable, find P(z>0.97) P ( z > 0.97 ) P(z>0.97)

Correct AnswerverifiedShow Answer

Correct Answerverified(i) people.(iii) The sample means tar...View AnswerShow Answer

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate P(6) for n=18 and p=0.3 .

Correct AnswerverifiedShow Answer

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distributed

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6. What are the values of the mean and standard deviation after all test scores have been standardized by converting them to z-scores using zx=−() μ /σ?

Correct AnswerverifiedShow Answer

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5 ?

Correct AnswerverifiedShow Answer

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Correct AnswerverifiedAssume that the random variable has a d...View AnswerShow Answer

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

Correct AnswerverifiedShow Answer

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what pattern would you expect in a normal quantile plot of these data?

Correct AnswerverifiedShow Answer

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

Correct AnswerverifiedShow Answer

If z is a standard normal variable, find the probability: P(−0.73<z<2.27) P ( - 0.73 < z < 2.27 ) P(−0.73<z<2.27)

Correct AnswerverifiedA

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

Correct AnswerverifiedB

Correct AnswerverifiedShow Answer

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of no more than 35 defective CDs

Correct AnswerverifiedShow Answer

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

Correct AnswerverifiedA density curve is a graph of a continuo...View AnswerShow Answer

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a<z<a) P ( - a < z < a ) P(−a<z<a) =0.4314 , find a.a .a.

Correct AnswerverifiedShow Answer

Scores on a test have a mean of 70 and Q3Q _ { 3 }Q3​ is 83 . The scores have a distribution that is approximately normal. Find P90P _ { 90 }P90​ (You will need to first find the standard deviation.)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
verified
Since the normal quartile plot...
View Answer

Correct Answer
verified

If z is a standard normal variable, find $P ( z > 0.97 )$

Correct Answer
verified

Correct Answer
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(i)
people.
(iii) The sample means tar...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
Assume that the random variable has a d...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

If z is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27 )$

Correct Answer
verified
A

Correct Answer
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B

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
A density curve is a graph of a continuo...
View Answer

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $P ( - a < z < a )$ =0.4314 , find $a .$

Correct Answer
verified

Scores on a test have a mean of 70 and $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ (You will need to first find the standard deviation.)

Correct Answer
verified

Correct Answer
verified