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*