31 You are reviewing applications for the admissions board o

31. You are reviewing applications for the admissions board of a college and notice that 5 students submitted CAT scores instead of the more popular DOG scores. Fortunately, you know that you can convert CAT scores to DOG scores (using z scores). The mean CAT score was 38 with a standard deviation of 6. The mean for the DOG was 50 with a standard deviation of 10. Convert each of the following CAT scores to their respective DOG scores. a. 26 b. 35 c. 44 d. 47

Solution

a)

Note that

z = (x(CAT) - u(CAT))/sigma(CAT)

Also,

z = (x(DOG) - u(DOG))/sigma(DOG)

Thus,

(x(CAT) - u(CAT))/sigma(CAT) = (x(DOG) - u(DOG))/sigma(DOG)

Thus,

x(DOG) = (x(CAT) - u(CAT))*sigma(DOG)/sigma(CAT) + u(DOG)

So, for x(CAT) = 26,

x(DOG) = (26 - 38)*10/6 + 50 = 30 [ANSWER]

*************************

b)

If x(CAT) = 35,

x(DOG) = (35 - 38)*10/6 + 50 = 45 [ANSWER]

***************************

c)

If x(CAT) = 44,

x(DOG) = (44 - 38)*10/6 + 50 = 60 [ANSWER]

***********************

D)

If x(CAT) = 47,

x(DOG) = (47 - 38)*10/6 + 50 = 65 [ANSWER]