MA260 Online Exam 4_04 December 2015 Solution

| December 8, 2016

Question
Online Exam 4_04

Question 1 of 20

5.0 Points

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

A. 123

B. 118

C. 112

D. 111

Question 2 of 20

5.0 Points

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 3 of 20

5.0 Points

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

Question 4 of 20

5.0 Points

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

D. None

Question 5 of 20

5.0 Points

A study of the amount of time it takes a mechanic to rebuild the

transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4

hours and the standard deviation is 1.77 hours. Assume that a random

sample of 40 mechanics is selected and the mean rebuild time of the

sample is computed. Assuming the mean times are normally distributed,

what percentage of sample means are greater than 7.7 hours?

A. 0.62%

B. 34.46%

C. 65.54%

D. 99.38%

Question 6 of 20

5.0 Points

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%

Question 7 of 20

5.0 Points

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%

Question 8 of 20

5.0 Points

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 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

B. 3

C. 4

D. 4.1

Question 10 of 20

5.0 Points

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%

Question 11 of 20

5.0 Points

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%

Question 12 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 13 of 20

5.0 Points

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 14 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 15 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 16 of 20

5.0 Points

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

5.0 Points

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 18 of 20

5.0 Points

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

Question 19 of 20

5.0 Points

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%

Question 20 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

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