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Maths advance questions (1 Viewer)

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I got 2.5% for part a and 81.5% for part b but the answers say something else. I dont know if i am wrong or the answers
 

Trebla

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I have moved this to the Maths forum along with your other threads. Going forward, please post Maths questions in the relevant Maths forums, not General Discussion. Thanks!
 

tickboom

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I think 2.5% makes sense for part a), since the standard deviation is 10, and for a normal distribution 95% of values fall within two standard deviations from the mean (so that would be 2.5% above 120 and 2.5% below 80). Was both your part a) and part b) marked as wrong? Or just part b)?
 

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I think 2.5% makes sense for part a), since the standard deviation is 10, and for a normal distribution 95% of values fall within two standard deviations from the mean (so that would be 2.5% above 120 and 2.5% below 80). Was both your part a) and part b) marked as wrong? Or just part b)?
part a for me was wrong and there wasn't any answers for part b. But i also feel like the answers are wrong in part a because they used 99.7% which only applies for Z score of 3 but in part A it is referring to Z score of 2
 

tickboom

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Yes, that is the precisely correct answer. The 95% between 2 standard deviations of the mean is just an approximation after all (it is exactly 95.45%).

The exact answer for part b) should be P(90 < X < 120) = P(X<120) - P(X<90) = 0.9772 - 0.1587 = 0.8185 (which is quite close to what you got).
 

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Yes, that is the precisely correct answer. The 95% between 2 standard deviations of the mean is just an approximation after all (it is exactly 95.45%).

The exact answer for part b) should be P(90 < X < 120) = P(X<120) - P(X<90) = 0.9772 - 0.1587 = 0.8185 (which is quite close to what you got).
Wait so was i correct for both part A and part B?
 

tickboom

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Wait so was i correct for both part A and part B?
I think you were close to being correct for part a), it's just that it looks like you used the 95% approximation, rather than using the exact rule. In other words, rather than P(X>120) = (1-0.95)/2 = 0.025, you should instead use the more precise: P(X>120) = (1-0.9545)/2 = 0.02275

Part b) it looks like you were close. Perhaps you just had a minor rounding error (0.8185 would round to 81.9%, not 81.5%). But it sounds like you've definitely got the basic concepts correct.
 

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I think you were close to being correct for part a), it's just that it looks like you used the 95% approximation, rather than using the exact rule. In other words, rather than P(X>120) = (1-0.95)/2 = 0.025, you should instead use the more precise: P(X>120) = (1-0.9545)/2 = 0.02275

Part b) it looks like you were close. Perhaps you just had a minor rounding error (0.8185 would round to 81.9%, not 81.5%). But it sounds like you've definitely got the basic concepts correct.
I don't know how you did it or which rule you followed but for the HSC formula sheet, it says Z scores between -1 to 1 is 68%, -2 to 2 is 95% and -3 to 3 is 99.7%. So i used these values to get my answer
 

tickboom

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I think we are using the same rules, just different z-tables (with different levels of precision). So at the end of the day, I think you were right on both questions, and the person who wrote the answer was probably just using a different z-table.
 

Fizsi

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I got 2.5% for part a and 81.5% for part b but the answers say something else. I dont know if i am wrong or the answers
I have just done this and think both your answers are correct-I got the same without looking at yours first
 

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