Jacob is a very curious student. He wants to find the average height of all giraffes at the Ohio zoo. He guesses that the average is 67 CM. Jacob wants to test his guess by taking a simple random sample of 100 giraffes from the Ohio Zoo and use the sample mean (X1) to try to estimate the true average height of a giraffe at the Ohio zoo.

i. Jacob fins that the average height of his sample is around 66 CM and the standard deviation is 3 CM. Make a 95% confidence interval for the true average height of a giraffe at the Ohio zoo. Based on this interval, is Jacob's guess of 67 CM still somewhat reasonable?

ii. Jacob finds some data that the height of the African and Asian giraffes at the Ohio zoo both have a mean of 66 CM and a SD of 4 CM. If Jacob wants to find another sample of 100 Asian giraffes (X2), [assuming X1 and X2 are independent & M = max(X1, X2)], what is P(M<67).

iii. Now, suppose Jacob made two 95% confidence intervals for the true mean of the height of giraffes at the Ohio zoo using two independent random sample of giraffes. What would be the probability that neither of the confidence intervals Jacob constructed are successful in covering the true mean height of the Ohio zoo giraffe.