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?

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 =

c) Bell shaped

d) P(X>414) = 0.0000

(almost uncertain event)

i believe it is 0.1m because the measurement of 30.4m limits how precise you can be

you can only be as precise as the least precise measurement