Discussion:
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 question.
A. 68%
B. 1005
C. 99.7%
D. 95%
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%
3. 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
4. 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
5. 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
6. 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%
7. 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
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)