# If light bulbs have lives - Expert Answers

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

A. About 25%

B. About 50%

C. About 75%

D. About 68%

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

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

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

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

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

B. 3

C. 4

D. 4.1

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

a) The amount of change held by a teacher at the end of each day for a year

b) The amount of pocket money held by each student at a mid-sized liberal arts college at a given time

c) The number of heads that show when two coins are tossed

A. a

B. b

C. c

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

A. 79.13%

B. 82.46%

C. 84.13%

D. 84.46%

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

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

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%

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks.

In 99.7% of the years, the precipitation in this city is between __________ and __________ inches.

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

A. 61.5, 82. 5

B. 82.5, 61.5

C. 61.5, 85.5

D. 63.5, 82.5

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%

Which of the following statements concerning areas under the standard normal curve is/are true?

a) If a z-score is negative, the area to its right is greater than 0.5.

b) If the area to the right of a z-score is less than 0.5, the z-score is negative.

c) If a z-score is positive, the area to its left is less than 0.5.

A. a, c

B. b, c

C. a, b

D. a

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

The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

A. About $46.30

B. About $43.30

C. About $43.40

D. about $43.20

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

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

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

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

A. About 25%

B. About 50%

C. About 75%

D. About 68%

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

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

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

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

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

B. 3

C. 4

D. 4.1

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

a) The amount of change held by a teacher at the end of each day for a year

b) The amount of pocket money held by each student at a mid-sized liberal arts college at a given time

c) The number of heads that show when two coins are tossed

A. a

B. b

C. c

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

A. 79.13%

B. 82.46%

C. 84.13%

D. 84.46%

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

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

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%

The annual precipitation for one city is normally distributed with a mean of 72 inches and a standard deviation of 3.5 inches. Fill in the blanks.

In 99.7% of the years, the precipitation in this city is between __________ and __________ inches.

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

A. 61.5, 82. 5

B. 82.5, 61.5

C. 61.5, 85.5

D. 63.5, 82.5

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%

Which of the following statements concerning areas under the standard normal curve is/are true?

a) If a z-score is negative, the area to its right is greater than 0.5.

b) If the area to the right of a z-score is less than 0.5, the z-score is negative.

c) If a z-score is positive, the area to its left is less than 0.5.

A. a, c

B. b, c

C. a, b

D. a

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

The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

A. About $46.30

B. About $43.30

C. About $43.40

D. about $43.20

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

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

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

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

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