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Exam 5: Normal Probability Distributions

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Question 21

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According to government data, the probability than an adult was never married is 19%. You randomly select 49 adults and ask if he or she was ever married. Decide whether you can use the normal distribution to approximate the binomial distribution, If so, find the mean and standard deviation, If not, explain why.

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use normal...

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Question 22

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A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use The normal distribution to approximate the binomial distribution.

A) 0.0823
B) 0.8577
C) 0.7967
D) 0.0606

E) A) and B)
F) A) and C)

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Question 23

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Provide an appropriate response. Use the Standard Normal Table to find the probability. -The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Out of 50 pregnancies, how many would you expect to last less than 250 days?

A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with an amount between 19.8 ounces and 20.2 ounces or are you more likely to select a sample of eight bottles with a mean amount between 19.8 ounces and 20.2 ounces? Explain.

Find the area under the standard normal curve to the left of z = 1.25.

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30 (Source: U.S. National Center for Health Statistics) . Levels above 200 warrant attention. What percent of teenage boys Have levels between 170 and 225?

Use the standard normal distribution to find P(z < -2.33 or z > 2.33) .

For the standard normal curve, find the z-score that corresponds to the first decile.

Scores on a test have a mean of 72 and a standard deviation of 12. Random samples of size 64 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean And standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution.

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 110. Find the z-score corresponding to this value.

For the standard normal curve, find the z-score that corresponds to the first quartile.

The monthly rents for studio apartments in a certain city have a mean of $920 and a standard deviation of $190. Random samples of size 30 are drawn from the population and the mean of each sample is determined.

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores.

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

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association) . If a sample of 50 individuals is randomly selected, find the Probability that the mean of the sample will be greater than 200 pounds.

Match the binomial probability $\mathrm { P } ( \mathrm { x } < 40 )$ with the correct statement.

Provide an appropriate response. Use the Standard Normal Table to find the probability. -The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30. Levels above 200 warrant attention. If 95 teenage boys are examined, how many would you expect to have cholesterol levels greater than 225?

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

The ACT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 22.2 and the standard deviation was 4.9. The test scores of four students selected at random are 16, 24, 9, and 35. a)Find the z-scores that correspond to each value. b)Determine whether any of the values are unusual.

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 11. An individualʹs IQ score is found to be 119. Find the z-score corresponding to this value.