Question

The next two questions 4-5 are based on the following information.

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8. 4.

What is the probability that a student scored below 91 on this exam?

(a) 0.9878 (b) 0.8185 (c) 0.9500 (d) 0.8616 5.

If the professor grades on a curve (i.e., gives As to the top 10 percent of the class, regardless of the score), are you better off with
(i) Option 1: a grade of 81 on this exam with a mean of 73 and a standard deviation of 8 or
(ii) Option 2: a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3?

(a) Option 1 (b) Option 2 (c) you are indifferent between the two.

Answer 1

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8

= 73 ; = 8.4

Here

P(x < 91) = P(x< 91; 73 ; 8.4)

z = (91 - 73)/8 = 2.143

P(x < 91) = P(z < 2.143) = 0.9878

(5)

Here we will find z score for each option

Option 1

z = (81 - 73)/8 = 1

Option 2

z= (68 - 62)/3 = 2

so here option 2 is more better than option 1 as z score is higher for option 2.