Question

Suppose x has a distribution with ? = 11 and ? = 8.

(a) If a random sample of size n = 48 is drawn, find ?_x, ?_x and P(11 ? x ? 13). (Round ?_x to two decimal places and the probability to four decimal places.)

?_x =

?_x =

P(11 ? x ? 13) =

(b) If a random sample of size n = 66 is drawn, find ?_x, ?_x and P(11 ? x ? 13). (Round ?_x to two decimal places and the probability to four decimal places.)

?_x =

?_x =

P(11 ? x ? 13) =

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

Answer 1

(a) If a random sample of size n = 48 is drawn

?x =11

?x

P(11 ? x ? 13)

=P[0<Z<1.73]

=0.9582-0.5......................using normal probability table.

=0.4882

(b) If a random sample of size n = 66 is drawn

?x =11

?x

P(11 ? x ? 13)

=P[0<Z<2.03]

=0.9788-0.5................................using normal probability table.

=0.4788

c)

The standard deviation of part (b) the same as part (a) because of the larger sample size. Therefore, the distribution about ?x narrower