Question

Suppose X is a normal random variable with μ = 600 and σ = 89. Find the values of the following probabilities. (Round your answers to four decimal places.)

(a) P(X < 700)

(b) P(X > 350)

(c) P(300 < X < 900)

Answer 1

(a) P(X<700)

Z-score for 700 = (700-600)/89 = 100/89 =1.12

From standard normal tables, P(Z<1.12) = 0.8686

P(X<700) = P(Z<1.12) = 0.8686

P(X<700) = 0.8686

(b) P(X>350) = 1-P(X 350)

Z-score for 350 = (350-600)/89 = -250/89 = -2.81

From standard normal tables, P(Z -2.81) = 0.0025

P(X 350) = P(Z -2.81) = 0.0025

P(X>350) = 1-P(X 350) = 1-0.0025 =0.9975

P(X>350) = 0.9975

(c) P(300 < X < 900) = P(X<900) - P(X<300)

Z-score for 900 = (900-600)/89 = 300/89 = 3.37 ; Z-score for 300 = (300-600)/89 = -300/89 = -3.37

From standard normal tables,

P(Z<3.37) = 0.9996 ; P(Z<-3.37) = 0.0004

P(X<900) = P(Z<3.37) = 0.9996 ; P(X<300)=P(Z<-3.37) = 0.0004

P(300 < X < 900) = P(X<900) - P(X<300) = 0.9996-0.0004=0.9992

P(300 < X < 900) = 0.9992