Question

Your math professor receives several student emails each day. The probability model shows the number of emails your professor receives from students in a given day.

# student emails	0	1	2	3	4	5
Probability	0.10	0.10	0.20	0.20	0.30	0.10

1. How many emails should your professor expect to receive daily? Round your result to the nearest hundredth.
2. What is the standard deviation of the number of emails your professor should expect to receive? Round to the nearest hundredth.
3. If it takes your professor an average of 7 minutes to reply to each email s/he receives, how many should your professor expect to spend responding to student emails in a given day?
4. Your English professor expects the same mean number of emails with the same standard deviation. What is the mean and standard deviation of the difference in the number of emails the professors will receive.

Mean:

Standard Deviation:

Answer 1

First, find the expected number of emails received from the given data. To calculate the standard deviation of the number of emails, find the variance of the number of emails. Expected response time can be calculated by the help of the expected number of emails received. The mean and standard deviation of the difference in the number of emails can be calculated with the help of mean and standard deviation derived from the above questions.