Find the 5th 25th 50th and 90th percentiles of a normal dist

Find the 5th, 25th, 50th, and 90th percentiles of a normal distribution, then create a problem that requires the use of the central limit theorem with the above mean and variance. Be sure to give the solution. Thanks for any help! Please show work.

Solution

Find the 5th, 25th, 50th, and 90th percentiles of a normal distribution, then create a problem that requires the use of the central limit theorem with the above mean and variance. Be sure to give the solution as well.

Mean =38

Variance =10

Sd =3.1623

5^th percentiles =32.8

25^th percentiles = 35.87

50^th percentiles = 38

90th percentiles =42.05

Problem: suppose we take 25 persons from this population what is the probability of sample mean greater than 39.

solution

P( x mean > 39) = P(z > ( 39-38/(3.1623/sqrt(25)) )

= p( z > 1.58)

=0.0571