There are two professors who teach introductory statistics at a certain college:

Question

There are two professors who teach introductory statistics at a certain college: Mr. B and Ms. S. They give similar exams on the first few chapters of the text. The distribution of grades for Mr. B’s class is approximately normal with mean µ 73 and standard deviation 4, while the distribution of grades for Ms. S’s class is also approximately normal with mean µ 81 and standard deviation 9.

a) One of Mr. B’s students earns 76, while one of Ms. S’s students earns 85. Based on z scores, which student has the higher grade?

b) What is the grade for Q3 in Ms. S’s class?

Explanation / Answer

z score =(X-mean)/std deviation

as z score is a measure of relative strength in a particular group. therefore higher the z score better is z score,

a) z score of Mr. B's student =(76-73)/4 =0.75

z score of Mr. S's student =(85-81)/9 =0.4444

as z score for Mr. B's student is higher; therefore Mr. B's student  has the higher grade

b) for Q3 z score =0.6745

hence correspoding score =mean+z*std deviation =81+0.6745*9=87.07

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