Question: The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution: x 4567 P(X = x) 0.2 0.4

The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:

x 4567 P(X = x) 0.2 0.4 0.3 0.1

(a) Find the mean μ and the variance σ2 of X.

(b) Find the mean μX¯ and the variance σ2 X¯ of the mean X¯ for random samples of 36 cherry puffs.

(c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 5.5.

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