Deck 10: The Normal Distributions

Question 1

A Normal density curve has which of the following properties?

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.

Answer 1

D

Question 2

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

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.

Answer 2

D

Question 3

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 smaller than 27.8 inches?

A)2.5%
B)5%
C)16%
D)32%

Answer 3

C

Question 4

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?

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

Question 5

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 your calculator, what percent of 1-year-old girls are longer than 31.4 inches?

A)32%
B)5%
C)2.5%
D)2.27%

Question 6

When using your calculator to find the area under the standard Normal curve that corresponds to a particular z score < a,

A)The mean = 0 and the standard deviation = 1.
B)The mean = 1 and the standard deviation = 0.
C)The lower bound = a
D)None of these choices is correct.

Question 7

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

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

Question 8

Using your calculator, what is the area under the standard Normal curve corresponding to Z > -2.62?

A)0.0044
B)0.0047
C)0.9953
D)0.9956

Question 9

Using your calculator, what is the area under the standard Normal curve corresponding to -0.5 < Z < 1.2?

A)0.3085
B)0.8849
C)0.5764
D)0.2815

Question 10

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.
What is the approximate probability that the pH measurement of a randomly selected water specimen is greater than 8.2?

A)0.2475
B)0.2525
C)0.7475
D)0.7525

Question 11

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.
What is the approximate probability that the pH measurement of a randomly selected water specimen is a value between 7.5 and 8.2?

A)0.3003
B)0.6997
C)0.9522
D)0.9902

Question 12

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

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

Question 13

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?

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

Question 14

Birth weights at a local hospital have a Normal distribution with a mean of 110 ounces and a standard deviation of 15 ounces.
What is the proportion of infants with birth weights between 125 ounces and 140 ounces?

A)0.819
B)0.636
C)0.477
D)0.136

Question 15

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?

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 16

The heights of adult males are approximately Normally distributed with a mean of 70 inches and a standard deviation of 3 inches. An adult male is categorized as "short" if he is less than 64 inches tall and categorized as "tall" if he is in the top 3% of adult males in terms of height.
What proportion of adult males is classified as short?

A)0.0228
B)0.2525
C)0.7475
D)0.9772

Question 17

The heights of adult males are approximately Normally distributed with a mean of 70 inches and a standard deviation of 3 inches. An adult male is categorized as "short" if he is less than 64 inches tall and categorized as "tall" if he is in the top 3% of adult males in terms of height.
How tall does an adult male need to be to be assigned to the "tall" category?

A)53.07 inches
B)64.36 inches
C)75.64 inches
D)86.93 inches

Question 18

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?

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

Question 19

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 proportion of these fish are larger than 86 centimeters in length?

A)0.0228
B)0.0548
C)0.1151
D)0.8849

Question 20

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. To ensure that the smallest 8% of the brook trout get thrown back, what should the lower cut-off be?

A)72.95 centimeters
B)75.00 centimeters
C)80.00 centimeters
D)87.03 centimeters

Question 21

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?

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

Question 22

Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l.
What is the probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l?

Question 23

Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l.
What serum albumin level do the lower 10% of adults have?

A)25.2 g/l
B)26.8 g/l
C)28.6 g/l
D)41.4 g/l

Question 24

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?

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

Question 25

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 between 9.75 and 9.85 kg?

A)0.6827
B)0.6171
C)0.3829
D)0.3173

Question 26

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 minimum total body protein that the upper 25% of adult men with cirrhosis have?

A)9.60 kg
B)9.70 kg
C)9.73 kg
D)9.87 kg

Question 27

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?

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 28

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 greater than 12 kg?

A)0.0013
B)0.9772
C)0.9973
D)0.9987

Question 29

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?

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

Question 30

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

Question 31

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 proportion of vitamin drops containing more than 60.75 mg of vitamin C?

A)7%
B)15%
C)69%
D)93%

Question 32

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?

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

Question 33

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 probability that a person produces more than 76.7% of the cholesterol in his or her body?

A)0.0003
B)0.0006
C)0.9997
D)1

Question 34

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?

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

Question 35

X has a Normal distribution with mean 50 and standard deviation 8. Which of the following statements is correct?

A)The probability P(X < 52) is slightly smaller than the probability P(X ≤ 52).
B)The probability P(X < 52) is equal to the probability P(X ≤ 52).
C)The probability P(X < 52) is slightly greater than the probability P(X ≤ 52).
D)The probability P(X < 52) could be very different from the probability P(X ≤ 52).

Question 36

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?

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

Question 37

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?

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

Question 38

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?

Question 39

A researcher was interested in the lengths of brook trout and obtained the following quantile-quantile plot for determining the Normality of the distribution:
Based on this graph, what is the best description of the data?

A)Standard Normal
B)Normal, but not standard Normal
C)Skewed left
D)Skewed right

Question 40

A researcher was interested in the survival times of brook trout after their exposure to increased levels of total dissolved solids. The following quantile-quantile plot was obtained:
Based on this graph, what is the best description of the data?

A)Standard Normal
B)Normal, but not standard Normal
C)Skewed left
D)Skewed right

Question 41

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?

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

Question 42

The following Normal quantile plot displays the brain volumes of 30 autistic children:
Based on this graph, what is the best description of brain volumes?

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

Question 43

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?

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.