Question

Exam Grades

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 91 ?

(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

Solution :

Given that ,

mean = = 72

standard deviation = = 11

P(x >91 ) = 1 - P(x <91 )

= 1 - P[(x - ) / < (91 - 72) /11 ]

= 1 - P(z <1.73 )

Using z table,

= 1 -0.9582

=0.0418

(B)

P(x <63 ) = P(( x -) / (63 - 72) /11 )

= P(z <-0.82 )

Using z table

= 0.2061

(C)

Using standard normal table,

P(Z < z) = 8%

=(Z < z) = 0.08

= P(Z <-1.41 ) = 0.08

z = -1.41

Using z-score formula  

x = z +

x = -1.41 *11+72

x =56.49

(D)

Using standard normal table,

P(Z > z) = 9%

= 1 - P(Z < z) = 0.09

= P(Z < z ) = 1 - 0.09

= P(Z < z ) = 0.91

= P(Z < 1.34) = 0.91  

z = 1.34

Using z-score formula  

x = z +

x =1.34 *11+72

x = 86.74