Question

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

Robert, 1.19	Juan, 1.78	Susan, –2.03
Joel, 0.00	Jan, –0.91	Linda, 1.79

STEP 1:	Which of these students scored above the mean? (Select all that apply.)
	JuanJoelJanRobertLindaSusan

STEP 2:	Which of these students scored on the mean? (Select all that apply.)
	JoelJanSusanRobertJuanLinda

STEP 3:	Which of these students scored below the mean? (Select all that apply.)
	RobertLindaJanJoelSusanJuan

STEP 4:	If the mean score was μ = 160 with standard deviation σ = 15, what was the final exam score for each student? (Round your answers to the nearest whole number.)
	Robert Juan Susan Joel Jan Linda

Answer 1

The college Physical Education Department offered an Advanced First Aid course last summer.

Let X be the the scores on the comprehensive final exam. X is normally distributed with mean and standard deviation

and the Z score of X given by is normally distributed with mean 0 and standard deviation 1.

Scores for some of the students are shown below.

Robert, 1.19	Juan, 1.78	Susan, –2.03
Joel, 0.00	Jan, –0.91	Linda, 1.79

STEP 1:	Which of these students scored above the mean? (Select all that apply.)
	Let x be the score of a student. If a z score is greater than 0, we can say That is, we can say that if z score is greater than 0, then the test scores are greater than mean We can see that Robert, 1.19         Juan, 1.78         Linda, 1.79 have z scores greater than 0 and hence have scored more than the mean ans: Juan Robert Linda

STEP 2:	Which of these students scored on the mean? (Select all that apply.)
	Let x be the score of a student. If a z score is = 0, we can say That is, we can say that if z score is equal to 0, then the test score is equal to mean Only Joel has a z score=0. ans: Joel

STEP 3:	Which of these students scored below the mean? (Select all that apply.)
	Let x be the score of a student. If a z score is less than 0, we can say That is, we can say that if z score is less than 0, then the test scores are less than mean The following have negative z scores      Susan, –2.03         Jan, –0.91 ans: Jan, Susan

STEP 4:	If the mean score was μ = 160 with standard deviation σ = 15, what was the final exam score for each student? (Round your answers to the nearest whole number.)
	Using the formula we can get the exam scores x for a z score z using z score Exam score x Robert 1.19 160+1.19*15=177.85 Juan 1.78 160+1.78*15=186.7 Susan -2.03 160+-2.03*15=129.55 Joel 0 160+0*15=160 Jan -0.91 160+-0.91*15=146.35 Linda 1.79 160+1.79*15=186.85 ans: final exam score Robert 178 Juan 187 Susan 130 Joel 160 Jan 146 Linda 187