Suppose x has a distribution with = 10 and = 2. (a) If a random sample of size n = 46 is drawn, find x, x and P(10 ≤ x ≤ 12). (Round x to two decimal places and the probability to four decimal places.)

x = ?
x = ?
P(10 ≤ x ≤ 12) = ?

(b) If a random sample of size n = 73 is drawn, find x, x and P(10 ≤ x ≤ 12). (Round x to two decimal places and the probability to four decimal places.)
x = ?
x = ?
P(10 ≤ x ≤ 12) = ?

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is part (a) because of the sample size. Therefore, the distribution about x is .