Satistics - determine the required sample size

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 5 IQ points of the true mean. Assume that standard deviation = 15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

mu =100, sd = 15

what sample size is needed so sample mean is with 5 of 100?? in the interval (95, 105)??

z score = 1.645 for 99% CI. use z tables

z = (x-mu)/sd/sqrn) = 105-100)/5/sqrn = 5sqrn/5 = sqrn = 1.645

n = 1.645^2 = 2.70625 = about a sample size of 3 required for CI (95,105)