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Economics – Business Finance

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

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

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 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

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%

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

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

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

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

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 area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%?

a) The percentage of scores between 120 and 130

b) The percentage of scores between 110 and 120

c) The percentage of scores between 80 and 90

d) The percentage of scores between 90 and 120

A. b

B. b,c

C.d

D. a, b

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

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

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

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

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

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 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

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%

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

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

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

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

21.335 and 34.665 is exact answer.

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 area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%?

a) The percentage of scores between 120 and 130

b) The percentage of scores between 110 and 120

c) The percentage of scores between 80 and 90

d) The percentage of scores between 90 and 120

A. b

B. b,c

C.d

D. a, b

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

43.258 is exact value. Hence, b is correct alternative.

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

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

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