Suppose x has a distribution with = 16 and = 10.

(a)

If a random sample of size n = 31 is drawn, find _x, _x and P(16 x 18). (Round _x to two decimal places and the probability to three decimal places.)

_x = _x= P(16 x 18)=

(b)

If a random sample of size n = 66 is drawn, find _x, _x and P(16 x 18). (Round _x to two decimal places and the probability to three decimal places.)

_x = _x= P(16 x 18)=

(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 ---Select--- the same as smaller than larger than part (a) because of the ---Select--- larger smaller same sample size. Therefore, the distribution about _x is ---Select--- the same narrower wider .