The heights of the population of students at a college are n

The heights of the population of students at a college are normally distributed with a mean of 68 inches (5 feet 8 inches), a standard deviation of 3 inches, and a sample size of 100 students.

Fill in the blank: The value of 99.5th percentile of the sample mean heights is ____ inches. (Give your answer to two decimal places.)

Solution

Mean ( u ) =68
Standard Deviation ( sd )=0.3
Number ( n ) = 100
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P ( Z < x ) = 0.995
Value of z to the cumulative probability of 0.995 from normal table is 2.576
P( x-u/s.d < x - 68/0.3 ) = 0.995
That is, ( x - 68/0.3 ) = 2.58
--> x = 2.58 * 0.3 + 68 = 68.7728                  

The value of 99.5th percentile of the sample mean heights is 68.77 inches