Question 1

Which of the following statements is true for the standard Normal curve?

Accepted Answer

A) It has a mean = 0 and a standard deviation = 1. 
B) It has a mean centered under the highest point of the curve. 
C) It has a standard deviation located at the point of curvature change on either side of the mean. 
D) All of these choices are correct. 
A) It has a mean = 0 and a standard deviation = 1. 
B) It has a mean centered under the highest point of the curve. 
C) It has a standard deviation located at the point of curvature change on either side of the mean. 
D) All of these choices are correct.

Question 2

The following Normal quantile plot displays the body temperature (in degrees Celsius) of a sample of 129 healthy adults:
  Based on this graph, what is the best description of the distribution of body temperatures?

Accepted Answer

A) Linear 
B) Roughly Normal 
C) Bimodal 
D) Skewed 
A) Linear 
B) Roughly Normal 
C) Bimodal 
D) Skewed

Question 3

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 microns.
What is the standardized score for a binding site position of 2.03 microns?

Accepted Answer

The answer of Using fluorescent imaging techniques, researchers observed that...

Question 4

The amount of cholesterol in a person's body produced by the liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%.
What is the first quartile of the distribution of cholesterol production?

Accepted Answer

A) 74.66% 
B) 75.00% 
C) 75.34% 
D) 75.50% 
A) 74.66% 
B) 75.00% 
C) 75.34% 
D) 75.50%

Question 5

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg.
We obtain the numerical value for P(X ≤ 9.65). Which of the following statements about the probability, P(X < 9.65), is true?

Accepted Answer

A) P(X < 9.65) has exactly the same value as P(X ≤ 9.65). 
B) P(X < 9.65) is slightly larger than P(X ≤ 9.65). 
C) P(X < 9.65) is slightly smaller than P(X ≤ 9.65). 
D) P(X < 9.65) could be slightly larger or slightly smaller than P(X ≤ 9.65), but we cannot tell without examining the population closely. 
A) P(X < 9.65) has exactly the same value as P(X ≤ 9.65). 
B) P(X < 9.65) is slightly larger than P(X ≤ 9.65). 
C) P(X < 9.65) is slightly smaller than P(X ≤ 9.65). 
D) P(X < 9.65) could be slightly larger or slightly smaller than P(X ≤ 9.65), but we cannot tell without examining the population closely.

Question 6

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg.
What is the approximate probability that a randomly selected healthy man has a total body protein between 12.1 and 12.2 kg?

Accepted Answer

A) 0.0228 
B) 0.1359 
C) 0.1587 
D) 0.3413 
A) 0.0228 
B) 0.1359 
C) 0.1587 
D) 0.3413

Question 7

The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3.
Three-fourths of the pH measurements in this river are greater than the value

Accepted Answer

A) 7.798. 
B) 8.202. 
C) 8.402. 
D) 8.450. 
A) 7.798. 
B) 8.202. 
C) 8.402. 
D) 8.450.

Question 8

The distribution of vitamin C amount in vitamin drops produced by a given factory is approximately Normal, with a mean of 60.0 mg and a standard deviation of 0.5 mg.
What is the approximate probability of drawing at random a vitamin drop with a vitamin content between 60.25 and 60.75 mg?

Accepted Answer

A) 0.16 
B) 0.24 
C) 0.38 
D) 0.62 
A) 0.16 
B) 0.24 
C) 0.38 
D) 0.62

Question 9

Using your calculator, what is the area under the standard Normal curve corresponding to Z < 1.15?

Accepted Answer

A) 0.1357 
B) 0.8643 
C) 0.8749 
D) 0.9332 
A) 0.1357 
B) 0.8643 
C) 0.8749 
D) 0.9332

Question 10

A Normal density curve has which of the following properties?

Accepted Answer

A) It is symmetric. 
B) It has a peak centered above its mean. 
C) The spread of the curve is proportional to the standard deviation. 
D) All of these choices are correct. 
A) It is symmetric. 
B) It has a peak centered above its mean. 
C) The spread of the curve is proportional to the standard deviation. 
D) All of these choices are correct.

Question 11

Birth weights at a local hospital have a Normal distribution with a mean of 110 ounces and a standard deviation of 15 ounces.
What proportion of infants have birth weights greater than 125 ounces?

Accepted Answer

A) 0.500 
B) 0.159 
C) 0.341 
D) 0.841 
A) 0.500 
B) 0.159 
C) 0.341 
D) 0.841

Question 12

The lengths of 1-year-old girls can be described using a Normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches.
Using the 68-95-99.7 rule, what percent of 1-year-old girls are longer than 31.4 inches?

Accepted Answer

A) 32% 
B) 5% 
C) 2.5% 
D) 0.0015% 
A) 32% 
B) 5% 
C) 2.5% 
D) 0.0015%

Question 13

A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. What is the probability of catching a brook trout less than 72 centimeters in length?

Accepted Answer

A) 0.0548 
B) 0.3745 
C) 0.6255 
D) 0.9452 
A) 0.0548 
B) 0.3745 
C) 0.6255 
D) 0.9452

Question 14

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg.
What is the minimum total body protein for the upper 75% of healthy adult men?

Accepted Answer

A) 12.10 kg or greater 
B) 12.18 kg or greater 
C) 12.23 kg or greater 
D) 12.37 kg or greater 
A) 12.10 kg or greater 
B) 12.18 kg or greater 
C) 12.23 kg or greater 
D) 12.37 kg or greater

Question 15

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron.
What is the probability that a binding site position is between 2.0 and 3.0 microns, approximately?

Accepted Answer

A) 0.785 
B) 0.843 
C) 0.902 
D) 0.942 
A) 0.785 
B) 0.843 
C) 0.902 
D) 0.942

Question 16

A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. The standard is set so that all fish smaller than 70.20 centimeters or larger than 89.80 centimeters must be thrown back. What proportion of the population would be thrown back?

Accepted Answer

A) 0.00 
B) 0.05 
C) 1.00 
D) 1.95 
A) 0.00 
B) 0.05 
C) 1.00 
D) 1.95

Question 17

A stemplot of a set of data is roughly symmetric, but the data do not even approximately follow the 68-95-99.7 rule. What should we conclude about the data?

Accepted Answer

A) They are Normal, but they are not standard Normal. 
B) They are standard Normal. 
C) They are not Normal. 
D) They are Normal. 
A) They are Normal, but they are not standard Normal. 
B) They are standard Normal. 
C) They are not Normal. 
D) They are Normal.

Question 18

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron.
What position (in microns) are 20% of binding sites greater than?

Accepted Answer

A) 2.0 microns 
B) 2.16 microns 
C) 2.74 microns 
D) 2.9 microns 
A) 2.0 microns 
B) 2.16 microns 
C) 2.74 microns 
D) 2.9 microns

Question 19

The birth weights of a random sample of 26 baby boys are displayed in the following Normal quantile plot:
  Based on this graph, what is the best description of the data?

Accepted Answer

A) The distribution has a low outlier. 
B) The distribution is approximately Normal. 
C) The distribution is skewed to the right. 
D) The distribution is bimodal. 
A) The distribution has a low outlier. 
B) The distribution is approximately Normal. 
C) The distribution is skewed to the right. 
D) The distribution is bimodal.

Question 20

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg.
What is the approximate probability that a randomly selected man with liver cirrhosis has a total body protein of 9.75 kg or greater?

Accepted Answer

A) 0.1915 
B) 0.3085 
C) 0.6914 
D) 0.8085 
A) 0.1915 
B) 0.3085 
C) 0.6914 
D) 0.8085

Exam 10: The Normal Distributions

Which of the following statements is true for the standard Normal curve?

The following Normal quantile plot displays the body temperature (in degrees Celsius) of a sample of 129 healthy adults: Based on this graph, what is the best description of the distribution of body temperatures?

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 microns. What is the standardized score for a binding site position of 2.03 microns?

The amount of cholesterol in a person's body produced by the liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%. What is the first quartile of the distribution of cholesterol production?

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. We obtain the numerical value for P(X ≤ 9.65). Which of the following statements about the probability, P(X < 9.65), is true?

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg. What is the approximate probability that a randomly selected healthy man has a total body protein between 12.1 and 12.2 kg?

The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3. Three-fourths of the pH measurements in this river are greater than the value

The distribution of vitamin C amount in vitamin drops produced by a given factory is approximately Normal, with a mean of 60.0 mg and a standard deviation of 0.5 mg. What is the approximate probability of drawing at random a vitamin drop with a vitamin content between 60.25 and 60.75 mg?

Using your calculator, what is the area under the standard Normal curve corresponding to Z < 1.15?

A Normal density curve has which of the following properties?

Birth weights at a local hospital have a Normal distribution with a mean of 110 ounces and a standard deviation of 15 ounces. What proportion of infants have birth weights greater than 125 ounces?

The lengths of 1-year-old girls can be described using a Normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches. Using the 68-95-99.7 rule, what percent of 1-year-old girls are longer than 31.4 inches?

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg. What is the minimum total body protein for the upper 75% of healthy adult men?

A stemplot of a set of data is roughly symmetric, but the data do not even approximately follow the 68-95-99.7 rule. What should we conclude about the data?

Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What position (in microns) are 20% of binding sites greater than?

The birth weights of a random sample of 26 baby boys are displayed in the following Normal quantile plot: Based on this graph, what is the best description of the data?

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. What is the approximate probability that a randomly selected man with liver cirrhosis has a total body protein of 9.75 kg or greater?

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Essential Probability Rules

Independence and Conditional Probabilities

Discrete Probability Distributions

Sampling Distributions

Introduction to Inference

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

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