5. Suppose the data concerning first-year salaries of graduates follows normal distribution with the population mean μ = $60, 000 and the stan- dard deviation σ = $10,000. Denote X as the salary of a

5. Suppose the data concerning first-year salaries of graduates follows normal distribution with the population mean μ = $60, 000 and the stan- dard deviation σ = $10,000. Denote X as the salary of a randomly selected graduate.

1. (a) What is the probability that X is greater than $40, 000?
2. (b) What is the probability that X is between $30, 000 and $90, 000?
3. (c) Suppose we interviewed 5 randomly selected SBU graduatesand their salaries are X1, X2, ..., X5. Denote the average salariesof these 5 people as X = X1 X2 X3 X4 X5 . What is the ex-5pectation and the variance of X?

(Hint: Use the standard normal table to answer (a) and (b).)