Question

A large group of students took a test in Statistics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students

a) scored between 50 and 90?

b) scored higher than 90?
c) should pass the test (grades≥50)

d)non of the above
d) should fail the test (grades<50)?

Answer 1

Let X be a random variable that represent the final grades of a large group of students.

where and  

Let   where  

a)

Percent of students scored between 50 and 90 = (100* 0.954)% = 95.4%

b)

Percent of student scored higher than 90 = (100* 0.023)% = 2.3%

c)  

Percent of students who should pass the test = (100* 0.977)% = 97.7%

d) None of the above means that the student fail the test i.e, his grades is less than 50

Percent of student who fail the test = (100* 0.023)% = 2.3%