Question 1

An accelerated life test on a large number of batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values? Explain the meaning of these two values.

Question 2

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds? Interpret the results qualitatively.

Question 3

The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month. The distribution of amounts spent is approximately normal with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

Question 4

Suppose the lengths of employment of the staff in a bank are normally distributed with mean 5.0 years and standard deviation 1.6 years. A simple random sample of 64 is drawn from the population.

a) What are the mean and the standard deviation of the distribution of the sample mean?
b) It is known that if the population is normally distributed then the sample mean is also normally distributed. What is the probability that the sample mean length of employment of staff will be (Interpret the results qualitatively)
(i) between 4.8 and 5.3 years
(ii) more than 4.5 years

Question 5

Acid rain, caused by the reaction of certain air pollutants with rainwater, appears to be a growing problem in the northeastern United States. (Acid rain affects the soil and causes corrosion on exposed metal surfaces.) Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). Suppose water samples from 40 rainfalls are analyzed for pH, and i and s are equal to 3.7 and 0.5, respectively.
a) Find a 99% confidence interval for the mean pH in rainfall and interpret the interval.
b) What assumption must be made for the confidence interval to be valid?
c) How can you estimate the results with a higher degree of accuracy?

Question 6

It is claimed that the average nicotine content of a cigarette does not exceed 17.5 milligrams. To test the claim, the nicotine contents in milligrams of 8 randomly selected cigarettes were examined.

21.0     16.2     21.5    20.9

15.7     16.3     17.8    19.4

Is it in line with the manufacturer's claim? Please interpret the statistical results in word. Use a 10% significance level.