Question 1

Solve the problem.
-The probability of no more than 35 defective CD's

Accepted Answer

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

Question 2

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
-Between 8.5 pounds and 10 pounds

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 3 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 3 }$

Question 3

Explain how a nonstandard normal distribution differs from the standard normal distribution. Describe the
process for finding probabilities for nonstandard normal distributions.

Accepted Answer

Both distributions are bell-shaped. In a

Question 4

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

Accepted Answer

A)  0.4168 
B)  0.5871 
C)  0.4641 
D)  0.0832 
A)  0.4168 
B)  0.5871 
C)  0.4641 
D)  0.0832

Question 5

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
-Shaded area is 0.0401.

Accepted Answer

A)  -1.63 
B)  -1.48 
C)  -1.89 
D)  -1.75 
A)  -1.63 
B)  -1.48 
C)  -1.89 
D)  -1.75

Question 6

The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Which of the following is true about the distribution of IQ scores?

Accepted Answer

A)  It is a standard normal distribution. 
B)  The area under its bell-shaped curve is 5. 
C)  The area under its bell-shaped curve is 1. 
D)  Its distribution is skewed to the left. 
A)  It is a standard normal distribution. 
B)  The area under its bell-shaped curve is 5. 
C)  The area under its bell-shaped curve is 1. 
D)  Its distribution is skewed to the left.

Question 7

Find the indicated probability.
-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)  0.5 
C)  0.0668 
D)  0.9332 
A)  0.4332 
B)  0.5 
C)  0.0668 
D)  0.9332

Question 8

After constructing a new manufacturing machine, five prototype integrated circuit chips are produced and it is
found that two are defective and three are acceptable. Assume that two of the chips are randomly selected with
replacement from this population. After identifying the 25 possible samples, find the proportion of defects in
each of them, using a table to describe the sampling distribution of the proportions of the defects.

Accepted Answer

The proportions have the probabilities s

Question 9

Solve the problem.
-Suppose that you wish to fin $\mathrm { P } ( - 2 < x < 2 )$

Accepted Answer

The answer obtained by using a normal di

Question 10

Find the indicated probability.
-The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

Accepted Answer

A)  0.4834 
B)  0.0179 
C)  0.9834 
D)  0.0166 
A)  0.4834 
B)  0.0179 
C)  0.9834 
D)  0.0166

Question 11

Solve the problem.
-In a population of 210 women, the heights of the women are normally distributed with a mean of 64.4 inches and a standard deviation of 2.9 inches. If 36 women are selected at random, find the mean $\mu _ { X } ^ { - }$ and standard
Deviation $\sigma _ { x }^ { - } $ of the population of sample means. Assume that the sampling is done without replacement and
Use a finite population correction factor.

Accepted Answer

A)  58.8 inches, 2.65 inches 
B)  64.4 inches, 2.07 inches 
C)  64.4 inches, 2.9 inches 
D)  64.4 inches, 0.44 inches 
A)  58.8 inches, 2.65 inches 
B)  64.4 inches, 2.07 inches 
C)  64.4 inches, 2.9 inches 
D)  64.4 inches, 0.44 inches

Question 12

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
-Shaded area is 0.0901.

Accepted Answer

A)  -1.26 
B)  -1.34 
C)  -1.45 
D)  -1.39 
A)  -1.26 
B)  -1.34 
C)  -1.45 
D)  -1.39

Question 13

Use the normal distribution to approximate the desired probability.
-Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or fewer arrive on time. Based on the result,
Does it seem plausible that the "on-time" rate of 74% could be correct?

Accepted Answer

A)  0.0316, no 
B)  0.0409, yes 
C)  0.0316, yes 
D)  0.0409, no 
A)  0.0316, no 
B)  0.0409, yes 
C)  0.0316, yes 
D)  0.0409, no

Question 14

Solve the problem.
-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

Solve the problem. -The probability of no more than 35 defective CD's

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. -Between 8.5 pounds and 10 pounds

Explain how a nonstandard normal distribution differs from the standard normal distribution. Describe the process for finding probabilities for nonstandard normal distributions.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -Shaded area is 0.0401.

The normal distribution has a greater percentage of its area close to the mean and much less in the tails. -Which of the following is true about the distribution of IQ scores?

Find the indicated probability. -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.

Solve the problem. -Suppose that you wish to fin $\mathrm { P } ( - 2 < x < 2 )$

Find the indicated probability. -The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -Shaded area is 0.0901.

Solve the problem. -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.

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

Exam 6: Normal Probability Distributions