Question

Suppose many classes took the same psychology exam and the average individual grade on the psychology exam is 70% (with a standard deviation of 10.4%). How much less likely is it to find a class (n=17) with an average on the psychology exam to be 75% than a single person with an average of 75% on the psychology exam?

Answer 1

Solution:

We are given

µ = 70

σ = 10.4

First find probability for individual score X, that is, P(X<75)

Z = (X - µ)/σ

Z = (75 - 70)/10.4

Z = 0.480769

P(Z<0.480769) = P(X<75) = 0.68466

(by using z-table)

Now find probability for average score X̄, that is, P(X̄<75)

Z = (X̄ - µ)/[σ/sqrt(n)]

Z = (75 – 70)/[10.4/sqrt(17)]

Z = 5/2.522371

Z = 1.982262

P(Z<1.982262) = P(X̄<75) = 0.976275

(by using z-table)

Difference in above two probabilities = 0.976275 - 0.68466 = 0.291615

So, it is approximately 29% less likely to find a class (n=17) with an average on the psychology exam to be 75% than a single person with an average of 75% on the psychology exam.