A large group of students took a test in Physics and the fin

A large group of students took a test in Physics 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 higher than 80?

b) should pass the test (grades?60)?

c) should fail the test (grades<60)?

Solution

a) For x = 80, z = 1

Area to the right (higher than) z = 1 is equal to 0.1586 = 15.87% scored more that 80.

b) For x = 60, z = -1

Area to the right of z = -1 is equal to 0.8413 = 84.13% should pass the test.

c)100% - 84.13% = 15.87% should fail the test.