1. Charlotte, North Carolina has a mean annual rainfall of 43 inches, with a standard deviation of 4.2 inches. We can assume that the amount of rainfall is Normally distributed.

A. What is the probability that, in a randomly selected year, Charlotte will receive between 40 and 46 inches of rain?

B. A UNCC student attends college in Charlotte for four years. What is the probability that the mean rainfall in these 4 years will be between 40 and 46 inches?

C. Why has the probability increased so dramatically from part (a) to part (b)?

1. Aynsleigh runs a business from home and ships items to her customers across the country. She advertises that her company ships 85% of its orders within two working days. She selects an SRS of 50 of the 1000 orders received in the past month to make sure her claim is true.

A. What is the mean of the sampling distribution of p ?

B. Find the standard deviation of the sampling distribution of p? Round to the nearest thousandth.

C. Draw the curve of the sampling distribution of p.

D. Of the 50 orders selected, only 82% were shipped within two days. What is the probability that the proportion of orders shipped on time is 82% or less?