Question

Question 10 1 pts Sarah is 29 and her mother Anne is 62. Sarah scores 135 on a standard IQ test and Anne scores 120 on the same test. The mean scores on this test for the 21 to 30 age group is 120 and standard deviation 15. The mean scores for the 61 to 70 age group is 110 and standard deviation 10. Which of the two has the higher IQ relative to her age group? Both did equally well relative to her age group Sarah - Anne Not enough information to calculate Submit Quiz No new data to save. Last checked at 2:22pm

Answer 1

Both did equally well relative to her age group.

Explanation:

Sarah's Age = 29 yrs

Anne's Age = 62 yrs

Sarah's IQ Score= 135

Anne's IQ Score = 120

Mean( Age 21-30 ) = 120

Standard Deviation ( Age 21 - 30) = 15

Mean ( Age 61 -70 ) = 110

Standard Deviation ( Age 61 - 70) = 10

We Know Sarah'age and Anne's age is 29 and 62, therefore belonging to Age group 21-30 and 61-70 respectively.

So, for Sarah, Mean and standard Deviation will be 120 and 15 respectively.

Also, for Anne, Mean and Standard Deviation will be 110 and 10 respectively.

For determining which one is better among their age group between Sarah and Anne, we will need to find z-score for both and whomever's z-score value will be greater will be better.

$z-score = \frac{x - \bar{x} }{s}$

where x = IQ score,

$\bar{x} = mean$

s = standard deviation

For SARAH,

$z-score = \frac{135-120}{15} = \frac{15}{15} = 1$

For ANNE,

$z-score = \frac{120-110}{10} = \frac{10}{10} = 1$

Both Sarah and Anne have same z-score, that means both of them did equally well in relative to her age group.