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TiliK225
2 months ago
7

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 \mu_{\bar X} and the variance \sigma^2_{\bar X} of the mean \bar 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.
Mathematics
1 answer:
Leona [12.6K]2 months ago
3 0

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.

Var(x) = 28.9-5.3^2=0.81

Standard deviation is the square root of the variance, which amounts to 0.9.

------------------------------------

b) For the mean of the sample, we find:

Mean = 5.3

Variance = var(x)/n = \frac{0.81}{{36} } \\=0.0225

c) P(\bar X

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