You and your friend decide throw a scrabble pizza party. You don't know how many pizzas to order, so you want to obtain an estimate of slices each person would eat. You perform a poll of ten randomly selected patrons to see how many slices they each ate. Their responses are Their responses are denoted Xi, i=1,...,10, and X=1/10 ∑10i=1Xi=4.3
s2=19∑10i=1(Xi−X)2=2.7

Assuming that the Xs are i. i.d. normal, construct a 95 confidence interval for the mean of the Xs.

1. Lower bound a
2. Upper bound b

How many patrons would you have had to poll to limit the width of the confidence interval to one slice?