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 2 of 20 5.0 Points
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 3 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 4 of 20 5.0 Points
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 5 of 20 5.0 Points
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
Question 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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 15 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 16 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 17 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 18 of 20 5.0 Points
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
Question 19 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 20 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%
ANSWERS
1.) C (2.87%)
2.) C ( 0.2417)
3.) D. 111
4.) C. (3.23)
5.) B. (b, c)
6. C. a and b
7. D. $132, $188
8. D. 83
9. B. b
10. B. b, d
11. B. b
12. A. 61.5, 82.5
13. D. 0.9192
14. B. 121.6, 150.4
15. D. 95%
16. C. 95%
17. D. 99.38%
18. B. About $43.30
19. D. a
20. D. 99.7%
Disclaimer: Credits to the owner of this test.
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