Question

A distribution of exam scores in History 101 for the past 10 years has a mean of 75. An exam score of 80 corresponds to a z-score of 0.5. What percentage of students in the past 10 years scored above a 60?

Answer 1

Solution:

Given:

Mean =

Examination Score = x = 80

z score = 0.5

We have to find:

P(  students in the past 10 years scored above a 60) =..........?

P( X > 60)=............?

Find z score for x = 60

But standard deviation is not given but can be obtained by given information:

For x = 80, z = 0.5

thus

Thus z score for x = 60

Thus we get:

P( X > 60)=P(Z > -1.50)

P( X > 60)=1 - P(Z < -1.50)

Look in z table for z = -1.5 and 0.00 and find corresponding area.

P( Z < -1.50) = 0.0668

Thus

P( X > 60)=1 - P(Z < -1.50)

P( X > 60)=1 - 0.0668

P( X > 60) = 0.9332

P( X > 60) = 93.32%

Thus 93.32% of students in the past 10 years scored above a 60