Given a normal distribution with Mu 53 and sigma 5 complet

Given a normal distribution with Mu = 53 and sigma = 5, complete parts (a) through (d). a. What is the probability that X > 45? P(X > 45) = b. What is the probability that X

Solution

mu = 53 , sigma = 5

a) P( X > 45) = P(z > (45- 53)/5) { converting into standard normal}

= P(Z> -1.6) = P(Z < 1.6) = 0.9452

b) P( X< 43) = P(z < (43- 53)/5) { converting into standard normal}

= P(Z < -2) = 1 - P(Z < 2) = 0.0227

c) 7% means 0.07

To find value let take 1- 0.07 = 0.93 at 0.93 value of Z is 1.48

then X = z* sigma + mu = 60.4