Question

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation

of 8. Which of the following questions below are of type B?

a. Find the 80th percentile.

b. Find the cutoff for the A grade if the top 10% get an A.

c. Find the percentage scoring more than 90.

d. Find the score that separates the bottom 30% from the top 70%.

e. Find the probability that a randomly selected student will score more than 80.

Answer 1

Let X be the test score

a)

Comparing both sides

x = 86.7328

# Z value for the probability 0.80 is calculated by Excel

=NORMSINV(probability)

b)

for cutoff for A grade we need to calculate the X value at 90%

comparing both sides

x = 90.2528

# Z value for the probability 0.90 is calculated by Excel

=NORMSINV(probability)

c)

  

= 1- 0.8944

=0.1056

=10.56%

# Probability for Z value 1.25 is calculated by Excel

=NORMSDIST(Z)

d)

For this we need to calculate the X value at 70%

Comparing both sides

x = 84.1952

e)

= 1- 0.5

= 0.5