Question

The final exam scores in freshman English at a large high school are normally distributed with a mean of 84% and a standard deviation of 14. If 450 students took the exam, approximately how many students scored between 70% and 80%? (please show work)
A. 103
B. 125
C. .2289
D. 99
E. 95

Answer 1

Answer:  A. 103

Step-by-step explanation:

Given : The final exam scores in freshman English at a large high school are normally distributed with a mean of 84% and a standard deviation of 14%.

i.e. $\mu=84\%$ and $\sigma=14\%$

Let x be the exam scores in freshman English ( in percent ).

Then, the probability that students scored between 70% and 80% would be

$P(70$

If 450 students took the exam, then the number of students scored between 70% and 80% = 450 x ( probability that students scored between 70% and 80%)

= 450 x 0.2289=103.005≈ 103

Therefore , About 103 students scored between 70% and 80% .

Hence, the correct answer is A. 103 .