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S2 MEI question... Please help me - I've been stuck all day!! watch

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    Please help me work out how to find the answer to this S2 question (taken from the S2 MEI Structured mathematics textbook pg. 54)

    The intelligence of an individual is frequently described by a positive integer known as an IQ (intelligence quotient). The distribution of IQs amongst children of a certain age-group can be approximated by a Normal probability model with mean 100 and standard deviation 15.

    A class of 30 children is selected at random from the age-group. Calculate (to 3 sig. fig) the probability that at least one member of the class has an IQ of 138 or more.

    (If you can help me, can you please show your working so that I know which method is being used. Thankyou so much!)
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    Could you estimate the probability that one specific child has an IQ of 138+, perhaps using tables? I would guess the answer to that is about 0.02

    Then the probability that the first child in the class (in alphabetical order say) has a lower IQ than this threshold is about 0.98
    and the same is true for each of the other 29

    So the probability that none of the 30 beats the 138 is 0.98^30 .. because independent

    So that probability that at least one has 138+ is 1 minus 0.98^30 .. but put in the proper value.
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    Okay notation sucks. anyway

    P(at least one child has IQ> 138)= 1-P(all children have IQ less than 138)
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    Thanks for your help. The answer in the back of the book is 0.165 (although they are sometimes wrong.) The question is in the 'approximating the binomial and poisson distribution section', so I've been trying to work it out that way - without success - because I don't know how to do it!!
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    Found it! Do you have a copy of MEI Formula and Tables? If so, p22 gives values for Normal Distribution. Is that idea new to you?
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    Me again: just looked on the MEI website. I think the topic you want is http://www.meiresources.org/resource...on_1/s2n1n.pdf
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    thankyou, I haven't got a log in though.
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    (Original post by ian.slater)
    Found it! Do you have a copy of MEI Formula and Tables? If so, p22 gives values for Normal Distribution. Is that idea new to you?

    Yep, I've got the tables. Do I need the inverse normal, or normal tables? So does the question not need any calculations but just looking at the tables? Thanks again for help
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    Oh my gosh!! I've done it!! Now going to try some more similar questions, so I might be back later!! Thankyou so so much everyone xxx

    Good luck if your S2 exam is on Monday!
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    Hi again: I've spent a while going through the S2 bit of the MEI website - I don't have a textbook. Looks like you're doing Ex2B Q01.

    Firstly, you have to get the idea of a 'continuity correction'. Because IQ is quoted to the nearest whole number, a score of 138 actually means a score of between 137.5 and 138.5. So we need to find the probability that IQ of a student (now assumed to be continuous) is >= 137.5.

    Cue fanfare of trumpets - 37.5 is exactly 2.5 * standard deviation of 15 in the question. So in the normal distribution tables on p22 of the booklet, you need to look up PHI(2.5) which is .9938 In other words 99.38% of students have IQ below 137.5 Or p(IQ>137.5) = 0.0062

    Now p(all students < 137.5) = 0.9938^30 which the MEI site gives as 0.830. Subtract this from 1 and you get 0.170.

    BUT I don't believe this is OK to 3 s.f. because the 0.0062 was only good for 2. But the method's sound, and the idea of continuity correction is core to the lesson you're meant to have just done.
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    it's no coincidence that that they tell you O(2.5) = 0.994 at the start of the question.
 
 
 
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