Deck 7: The Normal Probability Distributions

Question 1

High temperatures in a certain city for the month of August follow a uniform distribution over the interval to What is the probability that a randomly selected August day has a high temperature that exceeded

A) 0.1562
B) 0.4295
C) 0.0313
D) 0.8438

Answer 1

0.8438

Question 2

Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would

A) Have the same height but one would be shifted 4 units to the right.
B) Have no horizontal displacement but one would be flatter than the other.
C) Have no horizontal displacement but one would be steeper that the other.
D) Have the same height but one would be shifter 4 units to the left.

Answer 2

Have the same height but one would be shifted 4 units to the right.

Question 3

Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 0 and standard deviation of 0.5. The graphs would

A) Have the same height but one would be shifted 4 units to the right.
B) Have no horizontal displacement but one would be flatter than the other.
C) Have no horizontal displacement but one would be steeper that the other.
D) Have the same height but one would be shifter 4 units to the left.

Answer 3

Have no horizontal displacement but one would be steeper that the other.

Question 4

Draw a normal curve with ? = 60 and ? = 10. Label the mean and the inflection points.

A)
B)
C)
D)

Question 5

You are performing a study about the weight of preschoolers. A previous study found the weights to be normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool children and find their weights to be as follows. a) Draw a histogram to display the data. Is it reasonable to assume that the weights are normallydistributed? Why?
b) Find the mean and standard deviation of your sample.
c) Is there a high probability that the mean and standard deviation of your sample are consistentwith those found in previous studies? Explain your reasoning.

Question 6

The graph of a normal curve is given. Use the graph to identify the value of ? and ?.

A) ? = 12, ? = 9
B) ? = 3, ? = 12
C) ? = 12, ? = 3
D) ? = 9, ? = 12

Question 7

Determine whether the graph can represent a normal curve. If it cannot, explain why.

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A) The graph cannot represent a normal density function because it increases as x becomes very large or very small.
B) The graph can represent a normal density function.
C) The graph cannot represent a normal density function because it takes negative values for some values of x.
D) The graph cannot represent a normal density function because the area under the graph is greater than 1.

Question 8

Determine whether the graph can represent a normal curve. If it cannot, explain why.

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A) The graph cannot represent a normal density function because the area under the graph is greater than 1.
B) The graph cannot represent a normal density function because as x increases without bound, the graph takes negative values.
C) The graph cannot represent a normal density function because it has no inflection points.
D) The graph can represent a normal density function.

Question 9

Determine whether the graph can represent a normal curve. If it cannot, explain why.

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A) The graph cannot represent a normal density function because it is not bell shaped.
B) The graph cannot represent a normal density function because it does not approach the horizontal axis as x increases or decreases without bound.
C) The graph cannot represent a normal density function because it has no inflection points.
D) The graph can represent a normal density function.

Question 10

Determine whether the graph can represent a normal curve. If it cannot, explain why.

-

A) The graph cannot represent a normal density function because a normal density curve should approach but not reach the horizontal axis as x increases and decreases without bound.
B) The graph cannot represent a normal density function because it is bimodal.
C) The graph can represent a normal density function.
D) A and B are both true.

Question 11

The analytic scores on a standardized aptitude test are known to be normally distributed with mean and standard deviation (a) Draw a normal curve with the parameters labeled.
(b) Shade the region that represents the proportion of test takers who scored less than 725.
(c) Suppose the area under the normal curve to the left of X = 725 is 0.8413. Provide two interpretations of this result.

Question 12

Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right of

A) 0.3944
B) 0.1056
C) 0.7888
D) 0.2112

Question 13

Determine the area under the standard normal curve that lies between:

-z = 1 and z = 2

A) 0.1359
B) 0.8641
C) 0.000 8
D) 0.000 6

Question 14

Determine the area under the standard normal curve that lies between:

-z = 0.3 and z = 1.4

A) 0.3821
B) 0.6179
C) 0.9192
D) 0.3013

Question 15

Determine the area under the standard normal curve that lies between:

-z = -0.4 and z = 0.4

A) 0.5
B) 0.6554
C) 0.3446
D) 0.3108

Question 16

Determine the area under the standard normal curve that lies between:

-z = -2 and z = -0.7

A) 0.242
B) 0.2192
C) 0.758
D) 0.0228

Question 17

Find the indicated probability.

-Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(X < 70).

A) 0.8944
B) 0.9015
C) 0.8849
D) 0.1056

Question 18

Find the indicated probability.

-Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(X > 114).

A) 0.1977
B) 0.2420
C) 0.2119
D) 0.7881

Question 19

Find the indicated probability.

-Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P( 38 < X < 70).

A) 0.8944
B) 0.8914
C) 0.8819
D) 0.7888

Question 20

The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.36 ounces and a standard deviation of 0.24 ounce. The cans only hold 12.60 ounces of soda. Every can that has more than 12.60 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?

A) 0.1587
B) 0.8413
C) 0.6587
D) 0.3413

Question 21

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its left is 0.96

A) -1.38
B) 1.82
C) 1.75
D) 1.03

Question 22

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its left is 0.40

A) 0.57
B) -0.25
C) -0.57
D) 0.25

Question 23

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its left is 0.09.

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

Question 24

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its left is 0.04.

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

Question 25

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its left is 0.70.

A) 0.81
B) 0.53
C) 0.98
D) 0.47

Question 26

Find the indicated z-score.

-Find the z-score for which the area under the standard normal curve to its right is 0.70.

A) -0.53
B) -0.81
C) -0.47
D) -0.98

Question 27

Find the indicated z-score.

-Find the z-score having area 0.86 to its right under the standard normal curve; that is, find .

A) 0.5557
B) 1.08
C) -1.08
D) 0.8051

Question 28

Find the indicated z-score.

-Determine the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution.

A) -1.53, 1.53
B) -1.45, 1.45
C) -1.39, 1.39
D) -1.46, 1.46

Question 29

Find the indicated z-score.

-Determine the two z-scores that separate the middle 96% of the distribution from the area in the tails of the standard normal distribution.

A) -1.75 and 1.75
B) 0 and 2.05
C) -2.05 and 2.05
D) -2.33 and 2.33

Question 30

Find the indicated z-score.

-Find the z-scores for which 90% of the distribution's area lies between -z and z.

A) (-0.99, 0.99)
B) (-1.645, 1.645)
C) (-2.33, 2.33)
D) (-1.96, 1.96)

Question 31

Find the indicated z-score.

-Find the z-scores for which 98% of the distribution's area lies between -z and z.

A) (-2.33, 2.33)
B) (-1.645, 1.645)
C) (-0.99, 0.99)
D) (-1.96, 1.96)

Question 32

Find the value of.

-

A) 1.13
B) 0.55
C) 1.08
D) -1.13

Question 33

Find the indicated percentile.

-Assume that the random variable X is normally distributed with mean and standard deviation Find the 55th percentile for X.

A) 48.96
B) 51.04
C) 55.68
D) 52.8

Question 34

The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.06 ounce. Every can that has more than 12.15 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%?

A) 12.0198 oz
B) 12.2628 oz
C) 12.2802 oz
D) 12.0372 oz

Question 35

A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.14 ounce. The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)? Round to the nearest thousandth.

A) 12.304 oz
B) 12.002 oz
C) 12.340 oz
D) 12.001 oz

Question 36

Use a normal probability plot to asses whether the sample data could have come from a population that is normally distributed.

-An industrial psychologist conducted an experiment in which 40 employees that were identified as "chronically tardy" by their managers were divided into two groups of size 20. Group 1 participated in the new "It's Great to be Awake!" program, while Group 2 had their pay pay docked. The following data represent the number of minutes that employees in Group 1 were late for work after participating in the program.

A) not normally distributed
B) normally distributed