Question

Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions.

(a) What percent of students scored above a 92 ?

(b) What percent of students scored below a 63 ?
(c) If the lowest 8% of students will be required to attend peer tutoring sessions, what grade is the cutoff for being required to attend these sessions?

d) If the highest 9% of students will be given a grade of A, what is the cutoff to get an A?

Answer 1

Let x be the exam grades across all sections of introductory statistics at a large university.

x follows normal distribution with with mean ( µ ) = 72 and standard deviation (σ) = 11

a) P( x > 92) =

= P( z > 1.82 )

=1 - P( z ≤ 1.82 )

= 1 - 0.9656

= 0.034

b) P( x < 63 ) =

= P( z ≤ -0.83 )

= 0.2061

c) P( X ≤ x ) = 0.08

z score corresponding to 0.08 is -1.41

x = z*σ + µ

x = ( -1.41*11 ) + 72

x = 56.49

d) P( X > x ) = 0.09

P( X ≤ x ) = 1 - 0.09 = 0.91

z score corresponding to 0.91 is 1.34

A = z*σ + µ

A = ( 1.34*11 ) + 72

A = 86.74