Question

The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final were normally distributed, and the z scores for some of the students are shown below.
Robert, 0.96   Juan, 1.77   Susan, –2.01
Joel, 0.00   Jan, –0.91   Linda, 1.67
(a) Which of these students scored above the mean? (Select all that apply.)
Jan
Joel
Juan
Linda
Robert
Susan

(b) Which of these students scored on the mean? (Select all that apply.)
Jan
Joel
Juan
Linda
Robert
Susan

(c) Which of these students scored below the mean? (Select all that apply.)
Jan
Joel
Juan
Linda
Robert
Susan

(d) If the mean score was μ = 149 with standard deviation σ = 23, what was the final score for each student? (Round your answers to the nearest whole number.)
Robert  
Joel  
Jan  
Juan  
Susan  
Linda  

Answer 1

The mean of the normal distribution is 0.

(a) Students scoring above mean, i.e., greater than 0: Robert, Juan and Linda

(b) Students scoring on the mean, i.e., score of 0: Joel

(c) Students scoring below mean, i.e., score less than 0: Susan and Jan

(d) z-score for Robert is 0.96

0.96 = (X-149)/23 => X = 0.96 x 23 + 149 = 171.08

z-score for Juan is 1.77

1.77 = (X-149)/23 => X = 1.77 x 23 + 149 = 189.71

z-score for Susan is -2.01

-2.01 = (X-149)/23 => X = -2.01 x 23 + 149 = 102.77

z-score for Joel is 0

0 = (X-149)/23 => X = 0 x 23 + 149 = 149

z-score for Jan is -0.91

-0.91 = (X-149)/23 => X = -0.91 x 23 + 149 = 128.07

z-score for Linda is 1.67

1.67 = (X-149)/23 => X = 1.67 x 23 + 149 = 187.41

The scores are as below:

Student	Score
Robert	171.08
Joel	149
Jan	128.07
Juan	189.71
Susan	102.77
Linda	187.41