Question 1

If z is a standard normal variable, find the probability.
-The probability that z lies between -0.55 and 0.55

Accepted Answer

A)  -0.9000 
B)  0.4176 
C)  0.9000 
D)  -0.4176 
A)  -0.9000 
B)  0.4176 
C)  0.9000 
D)  -0.4176

Question 2

Solve the problem.
-In a certain population, 11% of people are left-handed. Suppose that you plan to randomly select 100 people and ask each person whether they are left handed. Suppose that in calculating each of the probabilities below,
You use the normal distribution as an approximation to the binomial but that you fail to use a continuity
Correction. In which cases will you obtain an answer that is too large? A: the probability that among the 100 people, at least 12 are left-handed B: the probability that among the 100 people, more than 12 are left-handed $C$ : the probability that among the 100 people, between 10 and 14 inclusive are left-handed

Accepted Answer

A)  A only 
B)  A and C 
C)  B only 
D)  B and C 
A)  A only 
B)  A and C 
C)  B only 
D)  B and C

Question 3

Solve the problem. Round to the nearest tenth unless indicated otherwise.
-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. Find P60, the score which separates the lower 60% from the top 40%.

Accepted Answer

A)  207.8 
B)  211.3 
C)  212.5 
D)  187.5 
A)  207.8 
B)  211.3 
C)  212.5 
D)  187.5

Question 4

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
-

Accepted Answer

A)  0.4656 
B)  -0.0344 
C)  0.9656 
D)  0.0344 
A)  0.4656 
B)  -0.0344 
C)  0.9656 
D)  0.0344

Question 5

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.
-More than 10 pounds

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 5 } { 6 }$

Question 6

Solve the problem.
-The probability that the number of correct answers is between 29 and 41 inclusive

Accepted Answer

A)  The area between 29.5 and 40.5 
B)  The area between 28.5 and 41.5 
C)  The area between 29 and 41 
D)  The area between 28.5 and 40.5 
A)  The area between 29.5 and 40.5 
B)  The area between 28.5 and 41.5 
C)  The area between 29 and 41 
D)  The area between 28.5 and 40.5

Question 7

Solve the problem.
-Samples of size n = 1500 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the proportion of odd numbers is found for each sample. What is the
Distribution of the sample proportions?

Accepted Answer

A)  not enough information provided 
B)  skewed to the left 
C)  normal (approximately) 
D)  skewed to the right 
A)  not enough information provided 
B)  skewed to the left 
C)  normal (approximately) 
D)  skewed to the right

Question 8

Solve the problem.
-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. If 50 different homes are randomly
Selected, find the probability that their mean energy consumption level for September is greater than 1075 kWh.

Accepted Answer

A)  0.4562 
B)  0.2090 
C)  0.2910 
D)  0.0438 
A)  0.4562 
B)  0.2090 
C)  0.2910 
D)  0.0438

Question 9

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

Question 10

What is the probability that the random variable has a value greater than 1.3?

Accepted Answer

A)  0.7875 
B)  0.7125 
C)  0.8375 
D)  0.9625 
A)  0.7875 
B)  0.7125 
C)  0.8375 
D)  0.9625

Question 11

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)  The mean is 50. 
B)  The mode is 100. 
C)  The standard deviation is 10. 
D)  The mean is 1. 
A)  The mean is 50. 
B)  The mode is 100. 
C)  The standard deviation is 10. 
D)  The mean is 1.

Question 12

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Accepted Answer

A)  0.0344 
B)  0.4656 
C)  -0.0344 
D)  0.9656 
A)  0.0344 
B)  0.4656 
C)  -0.0344 
D)  0.9656

Question 13

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

Accepted Answer

A)  0.4936 
B)  0.2946 
C)  0.1871 
D)  0.3229 
A)  0.4936 
B)  0.2946 
C)  0.1871 
D)  0.3229

Question 14

Solve the problem.
-The amount of rainfall (in inches) in 25 consecutive years in a certain city. $$\begin{array} { | l l l l l | } 
\hline 20.4 & 25.1 & 22.8 & 27.0 & 23.5 \
24.2 & 26.0 & 25.6 & 23.3 & 24.1 \
21.9 & 27.6 & 24.7 & 25.3 & 21.6 \
31.0 & 23.6 & 26.1 & 25.5 & 24.8 \
18.1 & 22.4 & 24.9 & 30.0 & 29.3 \
\hline
\end{array}$$

Accepted Answer

The requirement for normality

Question 15

Solve the problem.
-Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( \mathrm { z } > \mathrm { c } ) = 0.1093$ find c.

Accepted Answer

A)  0.4562 
B)  -1.23 
C)  0.27 
D)  1.23 
A)  0.4562 
B)  -1.23 
C)  0.27 
D)  1.23

Question 16

Which of the following is a biased estimator?

Accepted Answer

A)  mean 
B)  variance 
C)  proportion 
D)  standard deviation 
A)  mean 
B)  variance 
C)  proportion 
D)  standard deviation

Question 17

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.
-A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the reading that separates the bottom 4% from the others.

Accepted Answer

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

Question 18

Solve the problem.
-Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample median used to estimate a population median.

Accepted Answer

A)  biased 
B)  unbiased 
A)  biased 
B)  unbiased

Question 19

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Accepted Answer

A)  0.9331 
B)  0.0669 
C)  0.0769 
D)  0.0679 
A)  0.9331 
B)  0.0669 
C)  0.0769 
D)  0.0679

Question 20

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

If z is a standard normal variable, find the probability. -The probability that z lies between -0.55 and 0.55

Solve the problem. Round to the nearest tenth unless indicated otherwise. -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. Find P60, the score which separates the lower 60% from the top 40%.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -

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. -More than 10 pounds

Solve the problem. -The probability that the number of correct answers is between 29 and 41 inclusive

Solve the problem. -Samples of size n = 1500 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the proportion of odd numbers is found for each sample. What is the Distribution of the sample proportions?

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?

What is the probability that the random variable has a value greater than 1.3?

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 area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

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

Solve the problem. -The amount of rainfall (in inches) in 25 consecutive years in a certain city. 20.4 25.1 22.8 27.0 23.5 24.2 26.0 25.6 23.3 24.1 21.9 27.6 24.7 25.3 21.6 31.0 23.6 26.1 25.5 24.8 18.1 22.4 24.9 30.0 29.3

Solve the problem. -Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( \mathrm { z } > \mathrm { c } ) = 0.1093$ find c.

Which of the following is a biased estimator?

Solve the problem. -Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample median used to estimate a population median.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

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

If z is a standard normal variable, find the probability. -The probability that z lies between -0.55 and 0.55

Solve the problem. Round to the nearest tenth unless indicated otherwise. -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. Find P60, the score which separates the lower 60% from the top 40%.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -

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. -More than 10 pounds

Solve the problem. -The probability that the number of correct answers is between 29 and 41 inclusive

Solve the problem. -Samples of size n = 1500 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the proportion of odd numbers is found for each sample. What is the Distribution of the sample proportions?

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?

What is the probability that the random variable has a value greater than 1.3?

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 area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

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

Solve the problem. -The amount of rainfall (in inches) in 25 consecutive years in a certain city. 20.4 25.1 22.8 27.0 23.5 24.2 26.0 25.6 23.3 24.1 21.9 27.6 24.7 25.3 21.6 31.0 23.6 26.1 25.5 24.8 18.1 22.4 24.9 30.0 29.3

Solve the problem. -Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z>c)=0.1093\mathrm { P } ( \mathrm { z } > \mathrm { c } ) = 0.1093P(z>c)=0.1093 find c.

Which of the following is a biased estimator?

Solve the problem. -Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample median used to estimate a population median.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

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

Solve the problem. -Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $\mathrm { P } ( \mathrm { z } > \mathrm { c } ) = 0.1093$ find c.