Question

The scores on an exam are normally distributed, with a mean of 75 and a standard deviation of 5. What percent of the scores are less than 80?

A. 50%
B. 84%
C. 13.5%
D. 16%

Answer 1

B. 84%

Explanation:

Given

Mean= π=75

Standard Deviation= σ=5

As we have to calculate the percentage of score less than 80, we will find the z-score of 80

z=(x-μ)/σ

= (80-75)/5

=5/5

=1

The z-score table value for 1 is 0.8413.

For converting this value into percentage, the value will be multiplied by 100.

So,

Percentage of students whose score is less than 80 = 0.8413*100

=84.13%

Rounding off gives us : 84%

So option B is the correct answer..