A population of values has a distribution with

=

227.4

=227.4

and

=

50.1

=50.1

. You intend to draw a random sample of sizen

=

177

n=177

.

According to the Central Limit Theorem:

(a) What is the mean of the distribution of sample means?

x

=

x=

(b) What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

x

=

x=

(c) In a random sample of n=177, what is the probability that its sample mean is more than 235.1? Round to three decimal places.

(d) In a random sample of n=177, what is the probability that its sample mean is less than 227.3? Give your answer to three decimal places.