What proportion of the population is between 21 and 27 Round

What proportion of the population is between 21 and 27? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Solution

Normal Distribution
Mean ( u ) =21
Standard Deviation ( sd )=3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 27) = (27-21)/3
= 6/3 = 2
Z = 2
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 21) = (21-21)/3
= 0/3 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 27) = (27-21)/3
= 6/3 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(21 < X < 27) = 0.97725-0.5 = 0.4772                  
c)
P(X < 18) = (18-21)/3
= -3/3= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587