Consider a financial services salesperson whose annual salary consists of both a fixed portion of $25,000 and a variable portion that is a commission based on her sales performance. In particular, she estimates that her monthly sales commission can be represented by a random variable with mean $5000 and standard deviation $700.
a. What annual salary can this salesperson expect to earn?
b. Assuming that her sales commissions in different months are independent random variables, what is the standard deviation of her annual salary?
c. Between what two annual salary levels can this salesperson be approximately 95% sure that her true total earnings will fall?