A random sample of size 28 is to be selected from a populati

A random sample of size 28 is to be selected from a population that has a mean = 55 and a standard deviation of 17.

(A) What is the probability that this sample mean will be between 44 and 55? (Give your answer correct to four decimal places.)

(B) What is the probability that the sample mean will have a value greater than 48? (Give your answer correct to four decimal places.)

a) for x=44

z1= (44-55)/(17/sqrt(28)) = -3.423

for x=55 , z2=0

P(44<x,55) = P(z1<z<z2) = 0.500

b) for x=48

z=(48-55)/(17/sqrt(28)) = -2.178

P(x>48) = P(z>-2.178) = 0.9854