Chapter 5.4, Problem 42E

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.

42. Conservation About 74% of the residents in a town say that they are making an effort to conserve water or electricity. One hundred ten residents are randomly selected. What is the probability that the sample proportion making an effort to conserve water or electricity is greater than 80%? Interpret your result.