We want to compare the grades on an exam in an intro statist

We want to compare the grades on an exam in an intro statistics course for biology majorsversus public health majors. Suppose 72% percent of the class are biology majors. while theremaining 28% are public health majors. The biology majors earned grades that are normallydistributed. with a mean of 84 and a standard deviation of 10. The public health majors earned grades that are also normally distributed, with a mean of 87 and a standard deviation of 14. Of the students who didn?t make an A, what proportion were biology majors?

Solution

I presume that A is given over a score of 90.

Also, I assume a total strength of 100 for simplicity. Since only proportions are to be calculated, fractional values will be allowed.

Thus, 72 students are in Biology majors and 28 students are in public health majors.

For, biology:

P (X < 90) = P (Z < 90-84 /10)

= P (Z < 0.6)

= 0.7257

= 72.57%

= 52.25 students

similarly,

For public health majors,

P(X <90) = P(Z < 90 - 87 /14)

= P (Z < 0.2142)

= 0.5848

= 58.48%

= 16.37 students

Thus, from all those who couldn\'t make an A,

Biology majors = (52.25) / (52.25 + 16.37)

= 0.7614

Thus, out of students who did not get an A, 76.14% were biology majors.

Hope this helps.

In case, you are having troubles understanding fractional number of students, try taking the total strength to be 10,000 students instead and you should get the same answer.