Question

The average score on a standardized test is 750 points with a standard deviation of 50 points. If 2,000 students take the test at a local school, how many students do you expect to score between 700 and 750 points?

Answer 1

To get the expected value of student between 700 and 750 we proceed as follows;
z=(x-mean)/SD
thus;
z=(700-750)/50
z=-1
the probability associated with z=-1 is P(x)=0.1587
also;
z=(750-750)/50=0
the probability associated with z=0 is P(x)=0.5000
thus the probability of getting a number between 700 and 750 is:
0.5000-0.1587
=0.3413
thus the number of students students who scored between 700 and 750 will be:
0.3413*2000
=682.6
=683