Chapter 7. Question# 15, A population a has a mean of 200 and a standard deviation of 50. suppose a simple random sample of size 100 is selected and xbar is used to estimate µ.
a. what is the probability that the sample mean will be within + 5, or -5 of the population mean?
b. What is the probability that the sample mean will be within +10 or -10 pf the population mean?
Answer: we know µ=200. So we want the area between 195 and 205. Best use Excel for this. We have a sample (n=100) from a population. Because n>30, we can make use of the Central Limit Theorem. That means using =normdist in Excel. The standard error is 50/10 = 5. In Excel, first find the larger ‘x’ which is 205, then subtract the smaller one. So, the whole thing can be written in one line
=normdist(205,200,5,true)-normdist(195,200,5,true). I get 0.6827 for this. You can do the same for the second part of the question.