Whitney has STAT 225 office hours every Wednesday from 1:00 pm to 3:00 pm. The following table is the probability mass function for the number of students who stop by for help during Whitney's office hours, based on past experience. Let Xdenote the number of students who stop by during Whitney's office hours on a particular Wednesday.
| X |
Px(X) |
| 0 |
0.05 |
| 1 |
0.12 |
| 2 |
0.18 |
| 3 |
c |
| 4 |
0.16 |
| 5 |
0.23 |
a) Find the value of c that makes this a valid pmf.
b) What is the probability that Whitney will have no more than 3 students visit during his office hours?
c) How many students should Whitney expect to see during office hours?
d) What is the standard deviation of X?
e) Suppose each student will take exactly 20 minutes to ask questions during Whitney's office hours. What is the mean and variance of the time (in minutes) that Whitney spends on answering questions during his office hours?