a normal random variable x has a mean 14 and a standard devi

a normal random variable x has a mean =14 and a standard deviation =2. Find the probabilities of each value:

a. P(x>15.5)

b. P(x<11)

c. P(10<x<14.8)

Solution

MEAN = 14

SD =2

A)

For x = 11, z = (15.5 - 14) / 2 = 0.75

Hence P(x > 15.5) = P(z > 0.75) = [total area] - [area to the left of 0.75]

= 1 - 0.7734 = 0.2266

B)

For x = 11, the z-value z = (11 - 14) / 2 = -1.5

Hence P(x < 11) = P(z < -1.5) = [area to the left of 2.5] = 0.0668

C)