The Chapin Social Insight Test evaluates how accurately the

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are normally distributed with mean 25 and standard deviation 5.

A. What proportion of the population scores above 32 on the Chapin test? Please use 4 decimal places.
B.What proportion of the population scores below 10 on the Chapin test? Please use 4 decimal places.
C.How high a score must you have in order to be in the top 10% of the population in terms of score on the Chapin test? Please use 1 decimal place.

Please Show all work.

Solution

population mean,u = 25
standard deviation,sigma = 5

a.
P(X> 32 ) = P(Z> ((32-25) / 5)
= P(Z> 1.40 )
= 1 - P(Z<1.40)
= 1 - 0.9192
= 0.0808

b.
P(X< 10 ) = P(Z< ((10-25) / 5)
= P(Z< -3.00 )
= 1 - P(Z<3.00)
= 1 - 0.9987
= 0.0013

c.
P(X>k) = 0.10
P(X<k) = 0.90
P(Z<(k-u)/sigma) = 0.90

from table 0.90 = P(Z<1.28)
(k-u)/sigma = 1.28
k = 1.28*5 + 25
k = 31.4