Question

Question 4 (5 points)

The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard
deviation of 5 points
About what percent of students have scored between 55 and 65 points?

a. 2.5
b. 47.5
c. 68
d. 34​

Answer 1

Option C

Explanation:

Given

Mean= μ=60

and

Standard Deviation= σ=5

In order to calculate the percentage of students between 55 and 65, we have to calculate z-score for both

z-score for 55=(55-60)/5

=(-5)/5

=-1

The area to the left of z-score -1 is 0.1587

z-score for 65=(65-60)/5

=5/5

=1

The area to the left of z-score 1 is 0.8413

Area between z-scores of 55 and 65=0.8413-0.1587

=0.6826

Converting into percentage

=0.6826*100

=68.26%

Option C is the correct answer ..

Answer 2

c. 68

Explanation:

The empirical rule states that, if a population is approximately normal then 68% of the observations will fall within 1 standard deviation of the mean.

Going by this definition, 65 is one standard deviation to the right of the mean while 55 is one standard deviation to the left of the mean. Therefore, the percent of students who have scored between 55 and 65 points will be about 68%.

The question requires an approximation, About what percent, not exact computation. Thanks