Statistics

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 graduates
   and their salaries are X1, X2, ..., X5. Denote the average salaries
   of these 5 people as X = X1+X2+X3+X4+X5 . What is the ex-5
   pectation and the variance of X?

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