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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?

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Answer:

Step-by-step 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 = [tex]\frac{108}{\sqrt{216} } \\=7.348[/tex]

[tex]a) E(x) = 360\\b) Var(x) =7.348\\[/tex]

c) Bell shaped

d) P(X>414) = 0.0000

(almost uncertain event)

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