Question

A health Psychologist studies sugar consumption behavior. In his sample he measured the pounds of sugar a person consumed over a 6 month period. The sample measured n = 24 participants. It was a normally distributed data set with   M = 54 and   SD = 15

Calculate the Z scores for the following raw scores (X’s), also state the percentile ranking for each.  

A. X = 31  

B. X = 46

C. X = 28

D. X = 82

Answer 1

X~ Normal (54, 15)

a) X= 31

Z- score= = = -1.53

Percentile score = P( z < -1.53) = 1- P(z < 1.53) = 1- 0.93699 = 0.06301 = 6th percentile

b) X= 46

Z- score= = = -0.53

Percentile score = P( z < -0.53) = 1- P(z < 0.53) = 1-0.70194= 0.29806 = 30th percentile

c)X= 28

Z- score= = = -1.67

Percentile score = P( z < -1.67) = 1- P(z < 1.67) = 1-0.95254= 0.04746  = 5th percentile

d) X= 82

Z- score= = = 1.87

Percentile score = P( z < 1.87) = 0.96926 = 97th percentile