A random variable follows the normal probability distributio

A random variable follows the normal probability distribution with a mean of 118 and a standard deviation of 20.

A. What is the probably that a randomly selected value from this population is between 99 and 132?

B. What is the probability that a randomly selected value is between 74 and 93?

Solution

Normal Distribution
Mean ( u ) =118
Standard Deviation ( sd )=20
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 99) = (99-118)/20
= -19/20 = -0.95
= P ( Z <-0.95) From Standard Normal Table
= 0.17106
P(X < 132) = (132-118)/20
= 14/20 = 0.7
= P ( Z <0.7) From Standard Normal Table
= 0.75804
P(99 < X < 132) = 0.75804-0.17106 = 0.587                  

b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 74) = (74-118)/20
= -44/20 = -2.2
= P ( Z <-2.2) From Standard Normal Table
= 0.0139
P(X < 93) = (93-118)/20
= -25/20 = -1.25
= P ( Z <-1.25) From Standard Normal Table
= 0.10565
P(74 < X < 93) = 0.10565-0.0139 = 0.0917