We want to compare the grades on an introductory biology exam for freshman versu

Question

We want to compare the grades on an introductory biology exam for freshman versus sophomores. Suppose that 81% percent of the class are freshman, while the remaining are sophomores. The exam grades for freshman were normally distributed, with a mean of 81 and a standard deviation of 12. The exam grades for sophomores were also normally distributed, and 30% of the entire class got an “A” on the test (scored at least 90).

a. What grade corresponds to the 65th percentile of the distribution of freshman exam grades?

b. What proportion of sophomores got an “A” on the test?

c. If the standard deviation of exam grades for sophomores is the same as it is for freshman, what is the mean graph sophomores got on the exam?

Explanation / Answer

For P=65% =0.65, the z score is 0.39

=81

=12

x=z* +

=0.39*12 +81

=4.68+81

= 85.68

b)

first we try to find proportion of freshman who got A that is who got atleast 90

=81

=12

z=(x-)/

=(90-81)/12

=9/12

=0.75

P(x>90) =P(z>0.75)

              =1-P(z<0.75)

              =1-0.7734

              =0.2266

So proportion of freshman who got A is 0.2266*0.81 =0.183546

Hence proportion of sophomores =0.3-0.183546 =0.116454

out of 19%,proportion of sophomores who got A is 0.116454/0.19 =0.6129 or 61.29%

c)

z score for P=0.6129 is 0.2868

Hence,z=(x-)/

0.2868 =(90-)/12

3.4416=90-

=90-3.4416

=86.5584

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.