Answer following questions. (solve them by statistics formulas, don't use excel to solve these): 1)Let Z1, . . . , Z5 be independent and each have a standard normal distribution.

a) Specify the distribution of Z² 2 + Z² 3 + Z²4 + Z² 5

b) Specify the distribution of Z1 / (Z²2+Z²3+Z²4+Z²5)

2) Civil engineers collected data on the amount of salt needed to keep highways drivable during a snowstorm. 100 snowstorms required on average 1798.4 tons of salt with a standard deviation of 819.35 tons. Construct a 95% percent confidence interval for the true population mean amount of salt required for a snowstorm

3) If we want to determine the average mechanical aptitude of a large group of workers with a standard deviation of 20.0 points, how large a random sample will we need to assert with probability 0.95 that the sample mean will not differ from the true mean by more than 3.0 points?

4) Suppose that, the population of the amount of gold leave in a certain high-end component has = 8.4 square inches. We want to test the null hypothesis = 80 square inches against the alternative hypothesis < 80 square inches on the basis of a random sample of size n = 100. If the null hypothesis is rejected for a sample average below 78 square inches and otherwise it is accepted, determine

a) the probability of Type I error,

b) the probability of Type II error at = 76, and

c) the power of the test at = 76

5) In an air-pollution study, eight ozone measurements readings were :

7.9 11.3 6.9 12.7 13.2 8.8 9.3 10.6

Assuming the population sampled is normal, construct a 95% confidence interval for the mean.