Question

The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive test were normally distributed, and the z scores for some of the students are shown below.

Robert, 1.17 Juan, 1.76 Susan, –1.85 Joel, 0.00 Jan, –0.71 Linda, 1.64

(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 = 155 with standard deviation σ = 21, what was the test score for each student? (Round your answers to the nearest whole number.)

Robert

Joel

Jan

Juan

Susan

Linda

Answer 1

Answer a. All those students with Z score greater than 0 have scored above the mean score. They are:

Robert, Juan and Linda

Answer b. All the students who have Z score of 0 have scored on the mean score.

Only Joel have scored on the mean.

Answer c. All the students who have Z-score less than zero have score below the mean. They are:

Susan and Jan

Answer d.

Robert = 155 + 1.5*21 = 187

Joel = 155 +0*21 = 155

Jan = 155 -0.71*21 = 140

Juan = 155 + 1.76*21 = 192

Susan = 155 - 1.85*21 = 116

Linda = 155 +1.64*21 = 189