The Rolling Stones have toured extensively in support of new albums.  Pollstar has collected data on the earnings from the Stone's North American tours.  For 30 randomly selected Rolling Stones concerts, the mean gross earnings were $2.27 million.  Assume that the standard deviation for all earnings is $0.5 million.

1.  Does x-bar have a normal distribution?

Yes.  Since the sample size is 30, the CLT applies.

2. Compute a 99% confidence interval for the Stone's average earnings.

x-bar +/- z^*(sigma / sqrt(n))

2.27 +/- (2.576)(0.5 / sqrt(30))

2.27 +/- 0.235

3. How do you interpret this confidence interval?

We are 99% confident that the true mean earnings for the Stone's are between $2.035 million and $2.51 million.

4.  What sample size would be needed in order to estimate their average earnings to within +/-0.05 million dollars?

n = {(z^*)(sigma)/m}^2 = {(2.576)(0.5)/0.05}^2 = 663.5  => you need a sample size of 664