Question

assume that the MMPI Schizophrenia scale scores are normally distrbuted with mean of 50 and standard deviation of 10. what is the MMPI score at each of the following ranks(that is,precentages of individuals who score MMPI scores)

a. the MMPI score at the 90th precentile rank

b. the MMPI score at the 22th precentile rank

c. the MMPI score at the 50th precentile rank

Answer 1

Solution:-

Given that,

mean = = 50

standard deviation = = 10

a) Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90  

= P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 10 + 50

x = 62.8

90 th percentile MMPI score is = 62.8

b) Using standard normal table,

P(Z < z) = 22%

= P(Z < z) = 0.22

= P(Z < -0.77) = 0.22

z = -0.77

Using z-score formula,

x = z * +

x = -0.77 * 10 + 50

x = 42.3

22 th percentile MMPI score is = 42.3

c) Using standard normal table,

P(Z < z) = 50%

= P(Z < z) = 0.50

= P(Z < 0.00) = 0.50

z = 0.00

Using z-score formula,

x = z * +

x = 0.00 * 10 + 50

x = 50

50 th percentile MMPI score is = 50