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6.1 The Standard Normal Distribution

Rescaling any bell curve to mean zero and standard deviation one with z-scores, then reading tail areas from the resulting table.

Introductory Business Statistics 2e, 6.1 The Standard Normal Distribution

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25 exercises

6.1 Exercise 3

A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X = ____________.

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6.1 Exercise 5

X ~ N(1, 2)

σ = _______

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6.1 Exercise 7

X ~ N(–4, 1)

What is the median?

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6.1 Exercise 9

X ~ N(–2, 1)

μ = _______

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6.1 Exercise 11

What does standardizing a normal distribution do to the mean?

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6.1 Exercise 13

What is the z-score of x = 12, if it is two standard deviations to the right of the mean?

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6.1 Exercise 15

What is the z-score of x = –2, if it is 2.78 standard deviations to the right of the mean?

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6.1 Exercise 17

Suppose X ~ N(2, 6). What value of x has a z-score of three?

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6.1 Exercise 19

Suppose X ~ N(9, 5). What value of x has a z-score of –0.5?

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6.1 Exercise 21

Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?

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6.1 Exercise 23

Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean?

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6.1 Exercise 25

Suppose X ~ N(12, 6). What is the z-score of x = 2?

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6.1 Exercise 27

Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?

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6.1 Exercise 29

In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.

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6.1 Exercise 31

In a normal distribution, x = –5 and z = –3.14. This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.

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6.1 Exercise 33

About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?

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6.1 Exercise 35

About what percent of x values lie between the second and third standard deviations (both sides)?

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6.1 Exercise 37

Suppose X ~ N(–3, 1). Between what x values does 95.45% of the data lie? The range of x values is centered at the mean of the distribution(i.e., –3).

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6.1 Exercise 39

About what percent of x values lie between the mean and three standard deviations?

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6.1 Exercise 41

About what percent of x values lie between the first and second standard deviations from the mean (both sides)?

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6.1 Exercise 43

Use the following information to answer the next two exercises: The life of wearable fitness devicess is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A wearable fitness device is guaranteed for three years. We are interested in the length of time a wearable fitness device lasts.

Define the random variable X in words. X = _______________.

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6.1 Exercise 46

Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the z-score for a patient who takes ten days to recover?

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6.1 Exercise 48

The heights of the 430 National Basketball Association players were listed on team rosters at the start of a recent season. The heights of basketball players have an approximate normal di…

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6.1 Exercise 50

Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure…

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6.1 Exercise 52

During a certain year, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean µ = 520 and st…

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