The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:
| x |
4 |
5 |
6 |
7 |
| P(X=x) |
0.2 |
0.4 |
0.3 |
0.1 |
(a) Find the mean and variance of X.
(b) Find the probability that the number of cherries in a cherry puff will be no more than 5
(c) Find the probability that the average number of cherries in 36 cherry puffs will be no more than 5
(d) Find the probability that the average number of cherries in 36 cherry puffs will be greater than 5.5