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?