Question

The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. If 10,000 students take the exam, how many would you expect to score between 1700 and 1775 points?

Answer 1

Expected number of students, out of `10000` students, scoring a score between `1700` and `1750` is `2475`.

Explanation:

We have to find expected number of students (out of `10000` students), scoring a score between `1700` and `1750`. This is `10000` multiplied by the probability of scoring between `1700` and `1775` points given that distribution is normally distributed, with mean score of `1700` and standard deviation of `75` points.

Let us first calculate `z`-score for `1700` and `1775`. `z`-score for `1700` is `(1700-1700)/75=0` and for `1775` it is `(1750-1700)/75=50/75=0.6667`.

Hence probability of scoring between `1700` and `1775` points from tables is `0.2475`. (For more details see here. .)

Hence, expected number of students (out of `10000` students), scoring a score between `1700` and `1750` is `0.2475xx10000=2475`.