Question

(b) The mean score for a class sitting a Physics test is 46, with stan- dard deviation of 4. The mean score for the same class in a Chem- istry test is 77, with standard deviation of 9. Each set of scores is normally distributed. Which is more likely: a student gets over 90 on the Chemistry test, or over 52 on the Physics test? [7 marks

Answer 1

Explanation:

Let X be the mean score for physics test, and Y be the mean score for Chemistry test

Given that X is normal N(46,4)

Y is N(77,9)

when y>52 and x >90 to compare we have to convert these into corresponding Z scores

`x>52`⇒
`z>(52-46)/(4) \\z>1.5`

For
`y>90, \\Z>(90-77)/(9) =1.444`

Since Z>1.444 has more area than z>1.5 we find that it is more likely that

a student gets over 90 on the Chemistry test