# Expert Answers

1.) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side? Apply the 68-95-99.7 rule to this questions.

A. 68% B. 1005 C. 99.7% D. 95%

2.) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this question.

A. 68% B. 95% C. 100% D. 99.7%

3.) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

A. About 13.5% B. About 50% C. About 68% D. About 81.5%

4.) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

A. About 84% B. About 68% C. About 32% D. About 16%

Question 5 of 20 5.0 Points

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

A. 121.6, 152.4 B. 121.6, 150.4 C. 123.6, 150.4 D. 122.6, 148.4

Question 6 of 20 5.0 Points

A math teacher gives two different tests to measure students’ aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)

A. 87 B. 85 C. 86 D. 83

Question 7 of 20 5.0 Points

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

A. 0.4192 B. 0.5808 C. 0.0808 D. 0.9192

Question 8 of 20 5.0 Points

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

A. 0.8413 B. 0.3413 C. 0.3174 D. 0.1587

Question 9 of 20 5.0 Points

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

A. 2 B3 C4 D4.1

Question 10 of 20 5.0 Points

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

A. 19.46% B. 12.85% C. 2.87% D. 13.46

Question 11 of 20 5.0 Points

The amount of Jen’s monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks.

95% of her electric bills are between __________ and __________.

Apply the 68-95-99.7 rule to this question.

A. $140, $190 B. $132, $190 C. $140, $188 D. $132, $188

Question 12 of 20 5.0 Points

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

A. 62 B. 63 C. 63.5 D. 64

Question 13 of 20 5.0 Points

Which of the following statements concerning the standard normal curve is/are true (if any)?

a) The area under the standard normal curve to the left of -3 is zero.

b) The area under the standard normal curve between any two z-scores is greater than zero.

c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.

d) The area under the standard normal curve to the left of any z-score is less than 1.

A. a, b B. b, d C. a, c D. a

Question 14 of 20

Decide which of the described variables likely have a normal or near-normal distribution.

1. The number of credits remaining until graduation for the students in a small liberal arts college

2. The heights of male students in an advanced placement mathematics class

3. The number of sixes showing when two dice are rolled

A. a B. b C. c D. None

Question 15 of 20

A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275.

A. 0.2416 B. 0.2418 C. 0.2417 D. 0.2420

Question 16 of 20

Decide which of the described variables is/are likely to have a normal or near-normal distribution.

a) The heights of corn stalks in one row of corn that is half a mile long

b) The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values)

A. a B. b C. a and b D. neither

Question 17 of 20

The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks.

In 95% of the years, the precipitation in this city is between __________ and __________ inches.

Apply the 68-95-99.7 rule to this question.

A. 21.2, 34.8 B. 21.2, 34.6 C. 22.4, 34.6 D. 22.4, 34.8

Question 18 of 20

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

A. 0.9370 B. 0.6800 C. 0.6730 D. 0.0968

Question 19 of 20

At one college, GPA’s are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

A. 3.53 B. 3.42 C. 3.23 D. 3.13

Question 20 of 20

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this question.

A. 68% B. 99.7% C. 95% D. 100%

A. 68% B. 1005 C. 99.7% D. 95%

2.) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this question.

A. 68% B. 95% C. 100% D. 99.7%

3.) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

A. About 13.5% B. About 50% C. About 68% D. About 81.5%

4.) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

A. About 84% B. About 68% C. About 32% D. About 16%

Question 5 of 20 5.0 Points

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

A. 121.6, 152.4 B. 121.6, 150.4 C. 123.6, 150.4 D. 122.6, 148.4

Question 6 of 20 5.0 Points

A math teacher gives two different tests to measure students’ aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)

A. 87 B. 85 C. 86 D. 83

Question 7 of 20 5.0 Points

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

A. 0.4192 B. 0.5808 C. 0.0808 D. 0.9192

Question 8 of 20 5.0 Points

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

A. 0.8413 B. 0.3413 C. 0.3174 D. 0.1587

Question 9 of 20 5.0 Points

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

A. 2 B3 C4 D4.1

Question 10 of 20 5.0 Points

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

A. 19.46% B. 12.85% C. 2.87% D. 13.46

Question 11 of 20 5.0 Points

The amount of Jen’s monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks.

95% of her electric bills are between __________ and __________.

Apply the 68-95-99.7 rule to this question.

A. $140, $190 B. $132, $190 C. $140, $188 D. $132, $188

Question 12 of 20 5.0 Points

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

A. 62 B. 63 C. 63.5 D. 64

Question 13 of 20 5.0 Points

Which of the following statements concerning the standard normal curve is/are true (if any)?

a) The area under the standard normal curve to the left of -3 is zero.

b) The area under the standard normal curve between any two z-scores is greater than zero.

c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.

d) The area under the standard normal curve to the left of any z-score is less than 1.

A. a, b B. b, d C. a, c D. a

Question 14 of 20

Decide which of the described variables likely have a normal or near-normal distribution.

1. The number of credits remaining until graduation for the students in a small liberal arts college

2. The heights of male students in an advanced placement mathematics class

3. The number of sixes showing when two dice are rolled

A. a B. b C. c D. None

Question 15 of 20

A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275.

A. 0.2416 B. 0.2418 C. 0.2417 D. 0.2420

Question 16 of 20

Decide which of the described variables is/are likely to have a normal or near-normal distribution.

a) The heights of corn stalks in one row of corn that is half a mile long

b) The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values)

A. a B. b C. a and b D. neither

Question 17 of 20

The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks.

In 95% of the years, the precipitation in this city is between __________ and __________ inches.

Apply the 68-95-99.7 rule to this question.

A. 21.2, 34.8 B. 21.2, 34.6 C. 22.4, 34.6 D. 22.4, 34.8

Question 18 of 20

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

A. 0.9370 B. 0.6800 C. 0.6730 D. 0.0968

Question 19 of 20

At one college, GPA’s are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

A. 3.53 B. 3.42 C. 3.23 D. 3.13

Question 20 of 20

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

Apply the 68-95-99.7 rule to this question.

A. 68% B. 99.7% C. 95% D. 100%

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