A Biology Professor Responds to Some Student Questions by E-Mail

Essay

A biology professor responds to some student questions by e-mail. The probability model below describes the number of e-mails that the professor may receive from students during a day.

$\begin{array}{l|c|c|c|c|c|c} \text { E-mails received }& 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Probability} & 0.05 & 0.10 & 0.20 & 0.25 & 0.30 & 0.10\end{array}$

a. How many e-mails should the professor expect to receive each day?
b. What is the standard deviation?
c. If it takes the professor an average of ten minutes to respond to each e-mail, how much
time should the professor expect to spend responding to student e-mails each day?