Suppose that samples of size n 25 are selected at random fr

Suppose that samples of size n = 25 are selected at random from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from

Solution

Mean ( u ) =100
Standard Deviation ( sd )= 10/ Sqrt ( 25 ) = 2
Number ( n ) = 25              
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
So to the given normal distribution about 68% of the observations lie in between
=[100 ± 2 * 2]
= [ 100 - 4, 100 + 4 ] = [ 96,104]