Question

According to a study of the power quality​ (sags and​ swells) of a​ transformer, for transformers built for heavy​ industry, the distribution of the number of sags per week has a mean of 360 with a standard deviation of 108. Of interest is x overbar​, the sample mean number of sags per week for a random sample of 216 transformers. Complete parts a through d below.

a. Find E (x)
b. Find Var(x)
c. Describe the shape of the sampling distribution of x
d. How likely is it to observe a sample mean number of sags per week that exceeds 414?

Answer 1

Explanation:

Given that according to a study of the power quality​ (sags and​ swells) of a​ transformer, for transformers built for heavy​ industry, the distribution of the number of sags per week has a mean of 360 with a standard deviation of 108

Sample size n =216

By central limit theorem we have sample mean will follow a normal distribution with mean=360 and std deviation =
`(108)/(√(216) ) \\=7.348`

`a) E(x) = 360\\b) Var(x) =7.348\\`

c) Bell shaped

d) P(X>414) = 0.0000

(almost uncertain event)