Question

d. Suppose Professor Bernoulli has a policy of giving A’s to the top 10% of the scores on his final, regardless of the actual scores. If the distribution of scores on his final turns out to be normal with mean 69 and standard deviation 9, how high does your score have to be to earn an A? Show the appropriate calculations to support your answer. A (90-100%)

e. Professors Fermat and Gauss have final exam scores that are approximately normal with mean 75. The standard deviation of Fermat’s scores is 10 and that of Gauss’ is 5.

(1) With which professor is a score of 90 more impressive? Support your answer with appropriate calculations and with a sketch.

(2) With which professor is a score of 60 more discouraging? Support your answer with appropriate calculations and with a sketch.

Answer 1

(d)

= 69

= 9

Top 10% corresponds to area = 0.50 - 0.10 = 0.40 from mid value to Z on RHS.

Table of Area Under Standard Curve gives Z = 1.28

So,

Z = 1.28 = (X - 69)/9

So,

X = 69 + (1.28 X 9)

= 80.52

So,

Answer is:

80.52

(e)

(1)

Fermat:
= 75

= 10

X = 90

Z = (90 - 75)/10

= 1.50

Gauss:

= 75

= 5

X = 90

Z = (90 - 75)/5

= 3.00

So,

Gauss' score of 90 more impressive , because Z for Gauss = 3.00 is greater than Z for Fermat = 1.5

(2)

Fermat:
= 75

= 10

X = 60

Z = (60 - 75)/10

= - 1.50

Gauss:

= 75

= 5

X = 60

Z = (60 - 75)/5

= - 3.00

So,

Gauss' score of 60 more discouraging , because Z for Gauss = - 3.00 is less than Z for Fermat = - 1.5