The mean weight of 200 students in a certain college is 140

The mean weight of 200 students in a certain college is 140 lbs, and the standard deviation is 10 lbs. If we assume that the weights arc normally distributed, evaluate the following: The expected number of students that weigh between 110 and 145 lbs. The expected number of students that weigh less than 120 lbs. The expected number of students that weigh more than 170 lbs.

Solution

Normal Distribution
Mean ( u ) =140
Standard Deviation ( sd )=10
Normal Distribution = Z= X- u / sd ~ N(0,1)
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 110) = (110-140)/10
= -30/10 = -3
= P ( Z <-3) From Standard Normal Table
= 0.00135
P(X < 145) = (145-140)/10
= 5/10 = 0.5
= P ( Z <0.5) From Standard Normal Table
= 0.69146
P(110 < X < 145) = 0.69146-0.00135 = 0.6901                  
b)                  
P(X < 120) = (120-140)/10
= -20/10= -2
= P ( Z <-2) From Standard Normal Table
= 0.0228                  
c)
P(X > 170) = (170-140)/10
= 30/10 = 3
= P ( Z >3) From Standard Normal Table
= 0.0013