Assignment:
Question 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%
Question 2
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 3
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 4
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 5
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%
Question 6
The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?
A. 0.5012
B. 0.5010
C. 0.4015
D. 0.4013
Question 7
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 8
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 9
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 10
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 11
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 12
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 13
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 14
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 15
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 16
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 17
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 18
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 19
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 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