3 For a particular IQ test scores for people 20 to 34 years

3. For a particular IQ test, scores for people 20 to 34 years of age are normally distributed with a mean of 110 and a standard deviation of 25. Scores for the 60 to 64 age group are also normally distributed with a mean of 90 and a standard deviation of 25. Sarah who is 30 years old scored 130 on the IQ test while her mother who is 60 years old scored 115. a. What percentile does Sarah\'s score represent? Show your work. (5 pts) b. What percentile does Sarah\'s mother\'s score represent? Show your work. (5 pts) c. Who had a better performance on the IQ test? Circle your answer. (5 pts) 1) Sarah 2) Sarah\'s mother d. What score would be needed to be in the top 1.79% of scores for the 20 to 34 age group? Show all your work. (20 pts)

Solution

Sarah:
Mean = 110
Standard deviation = 25
x= 130

Sarah\'s Mother:
Mean = 90
Standard deviation = 25
x= 115

a) Find Z score;
Z score for Sarah

z= x-mu/sigma
=130-110/25
=0.8

So Sarah has scored at the 78.8th percentile

b) Z score for Sarah\'s mother

z= 115-90/25

=1

Sarah\'s mother has scored at the 84th percentile.

c) Sarah\'s mother\' score is \'Relatively Higher\'\'

But by considering the given raw scores, Sarah has scored higher in the variable measured.

Therefore, Sarah\'s mother performed better in IQ test.

d) Top 1.79%

0.9821 comes exactly between 2.33 and -2.33
As this is the top of scores
z= 2.33

To find x:

x= mu+ z*sigma

=110+ (2.33)(25)

= 168.25