Question

A. Scores on the Wechsler Intelligence Scale for Children (WISC) are standardized to be normally distributed with a mean of 100 and standard deviation of 15.

1.What is the WISC score of a child who scored 2 standard deviations above the mean?
2. What is the WISC score of a child who scored half a standard deviation below the mean?
3. What is the WISC score for a child whose z score was 0?

B. SAT-Math scores have a mean of 500 and standard deviation of 100. ACT-Math scores have a mean of 18 and standard deviation of 3. A student scored 640 on the SAT-Math and 22 on the ACT-Math. Compute the student’s z score for each test. On which test did they score more impressively? Explain why.

Answer 1

Solution:-

A)

Mean. = 100, S.D = 15

1) The WISC score of a child who scored 2 standard deviations above the mean is 130

z-score for two standard deviation above the mean = 2.0

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

$2= \frac{x-100 }{15 }$

x = 130
2) The WISC score of a child who scored half a standard deviation below the mean is 77.5

z-score for half a standard deviation below the mean = - 1.5

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

$-1.5= \frac{x-100 }{15 }$

x = 77.5

3) The WISC score for a child whose z score was 0 is 100.

z = 0

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

$0= \frac{x-100 }{15 }$

x = 100