Suppose that, on average, electricians earn approximately ? =54, 000 dollars per year in the United States. Assume that thedistribution for electricians' yearly earnings is normallydistributed and that the standard deviation is ? = 12, 000.
1. (3 points) What is the probability that a randomly selectedelectrician's salary is more than $50,000 but less than$60,000?
2. (3 points) Tax code dictates that 40% income tax is appliedto the electricians whose annual income is among top 5% in thepopulation. What is the minimum yearly earnings that will be leviedby 40% tax, i.e., ?nd the constant a such that Pr{X > a} =5%.
3. (3 points) In a sample of four electricians, what is theprobability that all four electricians' salaries are more than$50,000 but less than $60,000? (Please round your answer to 4decimal places.)
4. (3 points) In a sample of four electricians, let X ? be theaverage yearly earnings of these four electricians. What is theexpectation of the average earnings, i.e., E(X ?) =?
5. (3 points) In a sample of four electricians, let X ? be theaverage yearly earnings of these four 9electricians. What is thestandard deviation of the average earnings, i.e., s.e.(X ? ) =?
6. (3 points) Is the average earnings among four electricians, X?, normally distributed or not? Please explain. (No credit if thereis no explanation.)
7. (3 points) What is the probability that the average salary offour randomly selected electricians is more than $50,000 but lessthan $60,000, i,e, Pr{50, 000 < X ? < 60, 000}? (If you areable to ?nd this probability, please show your answer; if you arenot able to ?nd this probability, please explain why you cannot.)
8. (4 points) What is the probability that the average salary ofsixteen randomly selected electricians is more than $50,000 butless than $60,000 ? (If you are able to ?nd this probability,please show your answer; if you are not able to ?nd thisprobability, please explain why you can not.)
