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?
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
