1. (Determining the sample size for "rare" populations) Suppose you want to estimate the population mean for the variable "the number of hours that a child between the ages of 6 and 10 spends reading per week" in your hometown. You obtain a master file of residential addresses for your hometown. This master file only contains addresses, and nothing else. (Please assume that your hometown has more than 10,000 residential addresses, for example.) Your friend tells you that a previous survey from years ago on the same subject revealed a sample average of 13.3 and a sample standard deviation of 4.8 for the variable reading hours per week. She also tells you that only about 18% of the residential addresses in your hometown contain a family with a child between the ages of 6 and 10.

a) With that in mind, how many draws should you take from the masterfile if ultimately you would like your sample average estimate for reading hours per week to be within +/-6% from the true population mean with a probability of 90%?

Is it possible to solve this without using probabilities?