The heights of men have a normal distribution with mean mu

The heights of men have a normal distribution with mean mu = 67 inches and standard deviation sigma = 2 inches, Let X = height of a man. Find P (70

Solution

20)

P(70 < X < 72) = P(X < 72) - P(X < 70)

= P(Z < 72 -67/2) - P(Z < 70-67 /2)

= P(Z < 2.5) - P(Z < 1.5)

= 0.9938 - 0.9332

= 0.0606

21)

P(X > x) = 10%

= P(Z > x - 67 /2) = 10%

= x -67/2 = 1.2815

= 69.56

22)

P(X > 68)

= P(Z > 68 -67 /2/sqrt(16))

= P(Z > 2)

= 0.0228