Men in thirdworld countries have a life expectancy of mu 60

Men in third-world countries have a life expectancy of mu = 60 and sigma = 4.3. If a man in a third-world country lives to be 65 and a man in an industrialized country lives to be 72, who lived longer relative to their age distribution? In a distribution with a mean of 50 and a standard deviation of 5: What raw score corresponds with the 14^th percentile? What z-score cuts off the top 10% of this (or any) distribution? What raw score cuts off the top 10% of this distribution? What raw scores mark the middle 60% of this distribution?

Solution

11.

a)
P ( Z < x ) = 0.14
Value of z to the cumulative probability of 0.14 from normal table is -1.08
P( x-u/s.d < x - 50/5 ) = 0.14
That is, ( x - 50/5 ) = -1.08
--> x = -1.08 * 5 + 50 = 44.6                  

b)
Value of z to the cumulative probability of 0.1 from normal table is 1.28

c)
P ( Z > x ) = 0.1
Value of z to the cumulative probability of 0.1 from normal table is 1.28
P( x-u/ (s.d) > x - 50/5) = 0.1
That is, ( x - 50/5) = 1.28
--> x = 1.28 * 5+50 = 56.41