Question: a) Average weekly rate for graduates is $600 as claimed by Dean after graduation. The distribution of weekly incomes is Normal and has a standard deviation of $100.00, What is the probability that 25 randomly selected graduates have a wkly income less that 565.00. What assumptions are necessary for this analysis? Describe what kind of test this would be, if it were one.

b) Data may indicate salary is in fact less than $600. A random sample of 25 graduates had an average income of 567.17 . What would you conclude about the validity of the dean s’ claim at 5% significance level.

c) Find a 90% confidence interval for the true average weekly graduate income based on an average of $567.17 . Say clearly what this interval means in plain words

d) Using the confidence interval from question 2c above . State why it is not plausible for the true mean weekly income to be $600. Explain how the 90% confidence level test for the population is the Same as the one sided inferential test at 5% level that you did in question 2b.