Given a normal distribution with 104 and standard variatio

Given a normal distribution with ? = 104 and standard variation = 25, and given you select a sample of n=25.

Complete parts (a) through (d)

a.)What is the probability that X is less than 95?

b.) What is the probability that X is between 95 and 96.5?

c.) What is the probability that X is above 105.6?

d.) There is a 64% chance that X is above what value?

Solution

A) probability that X is less than 95 = P[Z < (95 - 104)/(25/sqrt(25)]

                                                          = P[Z < -1.8]

                                                          = 0.0359

B) P(95 < X < 96.5) = P[Z < (96.5 - 104)/(25/sqrt(25)] - [Z < (95 - 104)/(25/sqrt(25)]

                                                          = P[Z < -1.5] - P[Z < -1.8]

                                                          = 0.0668 - 0.0359 = 0.0309

C) P(X > 105.6) = 1 - P[Z < (105.6 - 104)/(25/sqrt(25)]

                          = 1 - P[Z < 0.32]

                          = 1 - 0.6255 = 0.3745

D) 64% implies z = 0.3585

0.3585 = (X - 104)/(25/sqrt(25))

X = 105.8