Question

The mean score was 72%. The standard deviation was 7%. Based on this information, what is the best approximation for the number of students who scored 80% or better?

Answer 1

Answer:

Option B. 159, is the correct answer

Step-by-step explanation:

Answer 2

Assuming scores (denoted by the random variable $X$) are normally distributed, we can say

$\mathbb P(X\ge80)=\mathbb P\left(\dfrac{X-72}7\ge\dfrac{80-72}7\right)\approx\mathbb P(Z\ge1.143)\approx0.1265$

where $Z$ has the standard normal distribution. So if there are $n$ students, we can expect approximately 12.65% of them to have a score of at least 80%.