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

Answer:

Step-by-step 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

$x>52$⇒$z>\frac{52-46}{4} \\z>1.5$

For $y>90, \\Z>\frac{90-77}{9} =1.444$

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