What proportion of the population is between 21 and 24 Round

What proportion of the population is between 21 and 24? (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.)

  
rev: 10_13_2011

Solution

Normal Distribution
Mean ( u ) =21
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 24) = (24-21)/5
= 3/5 = 0.6
Z = 0.6
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 21) = (21-21)/5
= 0/5 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 24) = (24-21)/5
= 3/5 = 0.6
= P ( Z <0.6) From Standard Normal Table
= 0.72575
P(21 < X < 24) = 0.72575-0.5 = 0.2257 ~ 22.57%              

c)
P(X < 18) = (18-21)/5
= -3/5= -0.6
= P ( Z <-0.6) From Standard Normal Table
= 0.2743 ~ 27.43