Consider a simple random sample of size 16 drawn from a norm

Consider a simple random sample of size 16 drawn from a normally distributed population with a mean of 80 and a standard deviation of 16. Find P(X > 85).

Solution

Mean ( u ) =80
Standard Deviation ( sd )=16
Number ( n ) = 16
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 85) = (85-80)/16/ Sqrt ( 16 )
= 5/4= 1.25
= P ( Z >1.25) From Standard Normal Table
= 0.1056