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.
1 answer:
Answer:
Step-by-step explanation:
The probability distribution for the random variable X is provided.
X 4 5 6 7 Total
P 0.2 0.4 0.3 0.1 1
x*p 0.8 2 1.8 0.7 5.3
x^2*p 3.2 10 10.8 4.9 28.9
a) The expected value E(X), representing the mean of X, equates to 5.3.
Standard deviation is the square root of the variance, which amounts to 0.9.
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b) For the mean of the sample, we find:
Mean = 5.3
Variance = var(x)/n =
c)
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