Chapter 5.4, Problem 41E

Sampling Distribution of Sample Proportions For a random sample of size n, the sample proportion is the number of individuals in the sample with a specified characteristic divided by the sample size. The sampling distribution of sample proportions is the distribution formed when sample proportions of size n are repeatedly taken from a population where the probability of an individual with a specified characteristic is p. The sampling distribution of sample proportions has a mean equal to the population proportion p and a standard deviation equal to $\sqrt{pq/n}$. In Exercises 41 and 42, assume the sampling distribution of sample proportions is a normal distribution.

41. Construction About 63% of the residents in a town are in favor of building a new high school. One hundred five residents are randomly selected. What is the probability that the sample proportion in favor of building a new school is less than 55%? Interpret your result.