Approx. how many students had scores of 89 or above?

[dwdrummerfreak]

The question reads as follows: "Scores on two exams are approximately normally distributed. Two hundred forty students took the Chemistry exam which had a mean of 76 and a standard deviation 14. Two hundred ten students took the Physics exam which had a mean of 72 and a standard deviation of 16. Approximately how many students, total, had scores of 89 or above?"

Answer choices:
a)65
b)72
c)77
d)84
e)91

I tried comparing the two means, but I only end up with a z-score, not one of the answer choices. I'm not quite sure how to go about answering this problem! Also, if you combine the two means, then how exactly would you find the scores of 89 or above? Any help would be very much appreciated! Thank You in advance!

 

[tkhunny]

Why are you comparing the means? What if the question had had only one exam? Could you have answered that?

Chemistry

z = (89-76)/14 = 0.929
Pr(z>0.929) = 0.176
240*0.176 = 42.24 So, 42ish

Okay, now throw in the other exam.

Physics

z = (89-72)/16 = 1.062
Pr(z>1.062) = 0.144
210*0.144 = 30.24 So, 30ish

42ish + 30ish = 72ishish

 

[dwdrummerfreak]

Thank You! You have been of much help! If it's not too much though, I would like to ask another quick question xD. How can you tell the difference between when you are using the central limit theorem, and when you are just using a z-test to standardize X? Thank You again!

 

[tkhunny]

In this case, we already know the population mean. The investigation is on specific examples.

 

[dwdrummerfreak]

Thank you once again!