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 of the random variable X.
(b) Find the standard deviation of the random variable X.
(c) Find the probability that the average number of cherries in 36 cherry puffs will not be less than 5.
(d) Find the probability that the difference in the average number of cherries in two randomly selected groups of 30 and 36 cherry puffs, respectively, will be more than 2