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Exam 5: Normal Probability Distributions

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Question 71

Multiple Choice

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For the standard normal curve, find the z-score that corresponds to the $7 ^ { \text {th } }$ decile.

A) 0.53
B) 0.98
C) 0.47
D) 0.12

E) B) and C)
F) None of the above

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Question 72

Multiple Choice

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Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 8. Compute the probability $\mathrm { P } ( 38 < \mathrm { X } < 70 )$

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

E) A) and B)
F) All of the above

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Question 73

Multiple Choice

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Find the area of the indicated region under the standard normal curve.

The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. If 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 Days and 266 days.

Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 12. Compute the probability $\mathrm { P } ( \mathrm { X } < 75 )$

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given Week the airline will lose between 10 and 20 suitcases?

Find the area under the standard normal curve between z = -1.5 and z = 2.5.

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height Between 63 and 65 inches.

The distribution of room and board expenses per year at a four-year college is normally distributed with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population And the mean of each sample is determined. Which of the following mean expenses would be considered Unusual?

Assume that the heights of women are normally distributed with a mean of 62.2 inches and a standard deviation of 2.3 inches. Find $\mathrm { Q } _ { 3 } ,$ the third quartile that separates the bottom 75% from the top 25%.

Decide if it is appropriate to use the normal distribution to approximate the random variable x for a binomial experiment with sample size of n = 48 and probability of success p = 0.6.

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $37,000 and a standard deviation of $5000. What is the cutoff salary for teachers in the bottom 10%?

Find the z-score that corresponds to the given area under the standard normal curve.

Find the area under the standard normal curve to the right of z = 1.

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If a woman is randomly selected, what is the probability that her height is between 58 and 80 inches?

Use the standard normal distribution to find P( $\mathrm { P } ( - 2.50 < \mathrm { z } < 1.50 )$

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 90. Find the z-score corresponding to this value.

Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find The percent of men meeting these height requirements.

The scores on a mathematics exam have a mean of 70 and a standard deviation of 5. Find the x-value that corresponds to the z-score 2.33.

Find the z-score that corresponds to the given area under the standard normal curve.