Heights of 18 yearold students have a bellshaped distributio

Heights of 18 year-old students have a bell-shaped distribution with mean 69 inches with standard deviation 2 inches. (use the empirical rule for both answers)

(a) about what proportion of students are between 67 and 57 inches tall?

(b) ) What interval centered on the mean contain about 95% of all such students?

? to ?

Solution

Normal Distribution
Mean ( u ) =69
Standard Deviation ( sd )=2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 57) = (57-69)/2
= -12/2 = -6
= P ( Z <-6) From Standard Normal Table
= 0
P(X < 67) = (67-69)/2
= -2/2 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(57 < X < 67) = 0.15866-0 = 0.1587   = 15.87% are in
between this 67 and 57 inches tall