Question

1) A student learns that on his most recent exam in environmental science, the sample mean was 67.08 with a standard deviation of 16.81. He scored a 75. If we assume that this is a population, and is normally distributed, what proportion of students in the class scored worse than this student? Enter your answer to four decimal places.

Answer 1

For above given problem

the sample mean is 67.08 with a standard deviation of 16.81

       = 67.08

and   = 16.81

A student scored a 75 on his most recent exam in environmental science

We want to find proportion of students in the class scored worse than this student

i.e   P ( < 75 )

Now = Z N ( 0 ,1 )

P ( < 75 )     =        =

                                                                          = P ( z < 0.4711481 )

From Normal probability table we find P ( z < 0.4711481 )

                       P ( z < 0.4711481 ) = 0.6812

Thus , proportion of students in the class scored worse than this student is 0.6812