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 μ and the variance σ² of x.(b) find the mean and the variance of the mean 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.

Step-by-step explanation:

Given is the probability distribution of a random variable X

X4567Total

P0.20.40.30.11

x*p0.821.80.75.3

x^2*p3.21010.84.928.9

a) E(X) = Mean of X = sum of xp = 5.3

Std dev = square root of variance = 0.9

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b) For sample mean we have

Mean = 5.3

Variance = var(x)/n =

c)

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

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