Question

4. Exam scores in Professor Curm’s Calculus class are approximately normally distributed with a mean of 71 and a standard deviation of 13. Exam scores in Professor Polly’s Calculus class are approximately normally distributed with a mean of 83 and a standard deviation of 7. Assume each class is made up of random draws from the same underlying student population, and so comparable in principle

.a) Compare a student who got a 68 in Curm’s class to one that got a 75 in Polly’s by calculating z scores and population percentiles. Use a z-table or excel or whatever software, as you wish, to calculate the percentiles.

b) What maintained assumption are you making?

Answer 1

a)

The z-score for student who got a 68 in Curm’s class is

The area left to z-score -0.23 using excel function "=NORMSDIST(-0.23)" is 0.4090.That is required percentile is 40.90th.

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The z-score for student who got a 75 in Polly’s class is

The area left to z-score -1.14 using excel function "=NORMSDIST(-1.14)" is 0.1271.That is required percentile is 12.71th.

Since .student who got a 68 in Curm’s class has higher percentile so student of Crum's class did better.

(b)

No assumption needed since it is given that scores are normally distributed