Question 1

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

Accepted Answer

A)  1.54 
B)  0.7557 
C)  0.4884 
D)  0.2211 
A)  1.54 
B)  0.7557 
C)  0.4884 
D)  0.2211

Question 2

Find the indicated probability.
-The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil
Will be less than 0.285 inches?

Accepted Answer

A)  0.4332 
B)  0.0596 
C)  0.0668 
D)  0.9332 
A)  0.4332 
B)  0.0596 
C)  0.0668 
D)  0.9332

Question 3

Use the normal distribution to approximate the desired probability.
-Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives.

Accepted Answer

A)  0.5871 
B)  0.7673 
C)  0.6229 
D)  0.8871 
A)  0.5871 
B)  0.7673 
C)  0.6229 
D)  0.8871

Question 4

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 $z = ( x - \mu ) / \sigma$ ?

Accepted Answer

A)  The mean is 10 and the standard deviation is 100. 
B)  The mean is 0 and the standard deviation is 1. 
C)  The mean is 100 and the standard deviation is 10. 
D)  The mean is 1 and the standard deviation is 0. 
A)  The mean is 10 and the standard deviation is 100. 
B)  The mean is 0 and the standard deviation is 1. 
C)  The mean is 100 and the standard deviation is 10. 
D)  The mean is 1 and the standard deviation is 0.

Question 5

Solve the problem.
-The heart rates (in beats per minute) of 30 randomly selected students are given below. $$\begin{array} { | l l l l l | } 
\hline 78 & 64 & 69 & 75 & 80 \
63 & 70 & 72 & 72 & 68 \
77 & 71 & 74 & 84 & 70 \
62 & 67 & 71 & 69 & 58 \
74 & 70 & 80 & 63 & 88 \
60 & 68 & 69 & 70 & 71
\end{array} \mid$$

Accepted Answer

The requirement for normality

Question 6

Use the normal distribution to approximate the desired probability.
-A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 16 tosses. What is the probability of being correct 16 or more
Times by guessing? Does this probability seem to verify her claim?

Accepted Answer

A)  0.0069, no 
B)  0.4931, yes 
C)  0.0069, yes 
D)  0.4931, no 
A)  0.0069, no 
B)  0.4931, yes 
C)  0.0069, yes 
D)  0.4931, no

Question 7

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of $0 ^ { \circ } \mathrm { C }$ at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some
give readings below $0 ^ { \circ } \mathrm { C }$ (denoted by negative numbers) and some give readings above $0 ^ { \circ } \mathrm { C }$ (denoted by positive
numbers). Assume that the mean reading is $0 ^ { \circ } \mathrm { C }$ and the standard deviation of the readings is $1.00 ^ { \circ } \mathrm { C }$ Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
-If 9% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

Accepted Answer

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

Question 8

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

Accepted Answer

An unbiased estimator is a statistic tha

Question 9

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find $P _ { 81 }$ , which separates the bottom 81% from the top 19%.

Accepted Answer

A)  0.291 
B)  66.6 
C)  73.5 
D)  0.88 
A)  0.291 
B)  66.6 
C)  73.5 
D)  0.88

Question 10

Solve the problem.
-A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,
Find the probability that their mean rebuild time exceeds 7.7 hours.

Accepted Answer

A)  0.9712 
B)  0.9931 
C)  0.9634 
D)  0.8531 
A)  0.9712 
B)  0.9931 
C)  0.9634 
D)  0.8531

Question 11

If z is a standard normal variable, find the probability.
-The probability that z lies between -1.10 and -0.36

Accepted Answer

A)  0.4951 
B)  -0.2237 
C)  0.2237 
D)  0.2239 
A)  0.4951 
B)  -0.2237 
C)  0.2237 
D)  0.2239

Question 12

Solve the problem.
-Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( - \mathrm { a } < \mathrm { z } < \mathrm { a } ) = 0.4314$ find a.

Accepted Answer

A)  0.3328 
B)  1.49 
C)  -0.18 
D)  0.57 
A)  0.3328 
B)  1.49 
C)  -0.18 
D)  0.57

Question 13

The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).

Accepted Answer

A)  0.7303 
B)  0.7938 
C)  0.7745 
D)  0.7619 
A)  0.7303 
B)  0.7938 
C)  0.7745 
D)  0.7619

Question 14

Use the normal distribution to approximate the desired probability.
-A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 11 tosses. What is the probability of being correct 11 or more
Times by guessing? Does this probability seem to verify her claim?

Accepted Answer

A)  0.4129, yes 
B)  0.0871, no 
C)  0.0871, yes 
D)  0.4129, no 
A)  0.4129, yes 
B)  0.0871, no 
C)  0.0871, yes 
D)  0.4129, no

Question 15

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal
distribution as an approximation.
-n = 24 and p = 0.6

Accepted Answer

A)  Normal approximation is not suitable. 
B)  Normal approximation is suitable. 
A)  Normal approximation is not suitable. 
B)  Normal approximation is suitable.

Question 16

Use the normal distribution to approximate the desired probability.
-Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Accepted Answer

A)  0.0871 
B)  0.1210 
C)  0.3871 
D)  0.2229 
A)  0.0871 
B)  0.1210 
C)  0.3871 
D)  0.2229

Question 17

Solve the problem.
-The weekly incomes (in dollars) of a sample of 12 nurses working at a Los Angeles hospital are given below. $$\begin{array} { | c c c c | } 
\hline 500 & 750 & 630 & 480 \
550 & 650 & 720 & 780 \
820 & 960 & 1200 & 770 \
\hline
\end{array}$$

Accepted Answer

@#IMG-DLM& Because the pattern of the po

Question 18

Find the indicated probability.
-The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

Accepted Answer

A)  0.2177 
B)  0.2823 
C)  0.1003 
D)  0.7823 
A)  0.2177 
B)  0.2823 
C)  0.1003 
D)  0.7823

Question 19

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

Question 20

Solve the problem.
-Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a
Mean replacement time less than 9.1 years.

Accepted Answer

A)  0.0643 
B)  0.0714 
C)  0.4357 
D)  0.4286 
A)  0.0643 
B)  0.0714 
C)  0.4357 
D)  0.4286

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

Find the indicated probability. -The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil Will be less than 0.285 inches?

Use the normal distribution to approximate the desired probability. -Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives.

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 $z = ( x - \mu ) / \sigma$ ?

Solve the problem. -The heart rates (in beats per minute) of 30 randomly selected students are given below. 78 64 69 75 80 63 70 72 72 68 77 71 74 84 70 62 67 71 69 58 74 70 80 63 88 60 68 69 70 71 \mid

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find $P _ { 81 }$ , which separates the bottom 81% from the top 19%.

If z is a standard normal variable, find the probability. -The probability that z lies between -1.10 and -0.36

Solve the problem. -Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( - \mathrm { a } < \mathrm { z } < \mathrm { a } ) = 0.4314$ find a.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. -n = 24 and p = 0.6

Use the normal distribution to approximate the desired probability. -Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Find the indicated probability. -The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

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.

Solve the problem. -Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a Mean replacement time less than 9.1 years.

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

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

Find the indicated probability. -The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil Will be less than 0.285 inches?

Use the normal distribution to approximate the desired probability. -Find the probability that in 200 tosses of a fair die, we will obtain at least 30 fives.

Solve the problem. -The heart rates (in beats per minute) of 30 randomly selected students are given below. 78 64 69 75 80 63 70 72 72 68 77 71 74 84 70 62 67 71 69 58 74 70 80 63 88 60 68 69 70 71 \mid

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find P81P _ { 81 }P81​ , which separates the bottom 81% from the top 19%.

If z is a standard normal variable, find the probability. -The probability that z lies between -1.10 and -0.36

Solve the problem. -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\mathrm { P } ( - \mathrm { a } < \mathrm { z } < \mathrm { a } ) = 0.4314P(−a<z<a)=0.4314 find a.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. -n = 24 and p = 0.6

Use the normal distribution to approximate the desired probability. -Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Solve the problem. -The weekly incomes (in dollars) of a sample of 12 nurses working at a Los Angeles hospital are given below. 500 750 630 480 550 650 720 780 820 960 1200 770

Find the indicated probability. -The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

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.

Solve the problem. -Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a Mean replacement time less than 9.1 years.

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

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find $P _ { 81 }$ , which separates the bottom 81% from the top 19%.

Solve the problem. -Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( - \mathrm { a } < \mathrm { z } < \mathrm { a } ) = 0.4314$ find a.