Chapter 5.3, Problem 5.23ACB

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality (sags and swells) of a transformer, Exercise 2.76 (p. 86). For transformers built for heavy industry, the distribution of the number of sags per week has a mean of 353 with a standard deviation of 30. Of interest is $\bar{x}$, the sample mean number of sags per week for a random sample of 45 transformers.

1. a. Find $E\left(\bar{x}\right)$ and interpret its value.
2. b. Find $\text{Var}\left(\bar{x}\right)$.
3. c. Describe the shape of the sampling distribution of $\bar{x}$.
4. d. How likely is it to observe a sample mean number of sags per week that exceeds 400?