In studying life spans of horses it was found using a sample of 30 boarded horses that the mean life span was 35.7 years. It is known that the population of all boarded horses lifespans has a standard deviation of s = 5 years.

a) (10 points) How many horses would be needed in a sample in order to estimate the mean lifespan for the population to within 3 months with a 99% level of confidence?

Hint: here, you are given the margin of error, E and the level of confidence, and you need to find the sample size required.

b) What is the level of confidence associated with a confidence interval of (43, 43.6) using the sample of 30 horses? (10 points)

Hint: here, you are given the margin of error, E because it is the radius of the confidence interval, so you know E = 0.3. And you know the sample size is 30, so you can use the