Statistics Question- z-score We want to compare the grades on an exam in an intr

Question

Statistics Question- z-score

We want to compare the grades on an exam in an intro statistics course for biology majors versus public health majors. Suppose 72% percent of the class are biology majors, while the remaining 28% are public health majors. The biology majors earned grades that are normally distributed, 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.

What exam score corresponds to the 80th percentile of the distribution for public health majors? (2pt)

What proportion of the class got an “A” on the test (scored at least 90)? (4pt)

Of the students who didn’t make an “A,” what proportion were biology majors? (4pt)

Explanation / Answer

72% Biology 28% Public health

Biology grades arenormal (84, 10)

Public health majors are normal (87,14)

80th percentile of std normal variable = 0.84

Hence corresponding x for 80th percentile =

87+14(0.84)

= 98.76

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Proportion for atleast 90=

Probability (X>90) for Biology

P(Z>0.6)

=0.2643

Similarly for PUblic health P(Y>90) = p(Z>3/14)

=P(Z>0.2143)

= 0.4168

Hence total class who got A would be

=0.72(0.2643)+0.28(0.4168)

= 0.1903+0.1167

= 0.3070

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Biology who did not make A = 1-0.2643

= 0.7357

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