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)

24

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24