Question

For a normal population with a mean of u=80 and a standard deviation of o=10, what is the probability of obtaining a sample mean less than M=81 for a sample of n=25 scores? Express your answer as a percentage (rounded to two decimal places)

Answer 1

Solution:

Given, the Normal distribution with,

   = 80

= 10

Sample of 25 is taken.

n= 25

Let be the sample mean.we know the distribution of is normal with

Mean() = = 80

SD() = = 10/​25 = 2.00 (It is called as the standard error of the mean)

P( < 81) =

=   

= P(Z < 0.50)

P( < 81) = 0.6915 .....use z table.

In percentage , P( < 81) = 69.15%