# Question: consider a large population of interest its distribution is normal...

###### Question details

Consider a large population of interest. It's distribution is normal and it's mean is 176 and standard deviation is 101. Let X = a single observation.

(Round all probabilities to four decimals)

a) Find P(X < 181):

A random sample of 148 is taken. Let X¯¯¯X¯ = sample average of the observations.

b) Find P(X¯¯¯X¯ < 181):

Consider another large population of interest. It's distribution
is *unknown* and it's mean is 176 and it standard deviation
is 101. Let Y = a single observation.

A random sample of 148 is taken. Let Y¯¯¯Y¯= sample average of the observations.

c) Find P(Y¯¯¯Y¯ < 181):