Maths

A farmer finds that the weights of sheep on his farm have a normal distribution with mean 66.4 kg
and standard deviation 5.6 kg.
250 sheep are chosen at random. Estimate the number of sheep which have a weight of between
70 kg and 72.5 kg.

Why there is no use of continuity correction in this question?And please show full solution of the question.

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  1. This question is referring to your z-scores : )
    You need your z score formula z=(x- mean/standard deviation
    You will find your z score for 72.5 and then a second z-score of 70
    and since the z-score table reads "less than" you will need to subtract the value of z found at 70 from the value of z found at 72.5
    This will give you the percent between 70 adn 72.5
    then you will have to multiply that percent by your 250 sheep to see how many would be between those weights.
    Your job is to follow these steps and produce a solution.

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    Ms Pi 3.14159265358979323
  2. Why can't we use P((72-66.4)/5.6) -(P(69.5-66.4)/5.6)?

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  3. If you are still using "tables", take a look at this webpage,
    which is probably the best for your type of question.

    http://davidmlane.com/normal.html

    You can bypass the z-score calculations and use the data
    directly as it is given to you, although the z-scores you calculated
    can be used as well. As a matter of fact , the default is a mean of 0 and
    a SD of 1

    Using the data as is, the result is .1221
    I clicked on the 'between' button then entered 70 and 72.5

    Using the z-scores that "Ms Pi" outlined, you would have....
    for 70: z-score = (70-66.4)/5.6 = .642857...
    and from your table you should get P(z < 70) = 0.7398
    for 72.5" z-score = (72.5-66.4)/5.6 = 1.08928..
    and from your table you should get P(z < 72.5) = .862

    so P( 70 < x < 72.5) = .862 - .7398 = .1222, same as before

    You then ask: Why can't we use P((72-66.4)/5.6) - (P(69.5-66.4)/5.6)??
    I don't know where you are getting your last P(69.5-66.4)/5.6) from?
    Is 69.5 a typo?
    Anyway, that is in effect what I did, let me know if this made sense to you.

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    Reiny
  4. Why do think it is a typo?I made that step intentionally.

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  5. And for the P((72-66.4)/5.6), I am getting probability 1.

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  6. makes no sense...

    for 72.5" z-score = (72.5-66.4)/5.6 = 1.08928..
    Now find 1.08928 in your table (or use my webpage)
    Here is a table:
    https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
    and from your table you should get P(z < 72.5) = .862
    The table I gave you should give you .86214, but I had to round 1.08928 to 1.09

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    Reiny
  7. As normal approximation to binomial,shouldn't it be P(X<72) for P(X<72.5) and P(X<69.5) for P(X<70) while continuity correction?

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  8. "As normal approximation to binomial,shouldn't it be P(X<72) for P(X<72.5) and P(X<69.5) for P(X<70) while continuity correction?"

    Must admit that I don't understand what that procedure is.
    The last time I taught this, 35 years ago, I never came across that terminology.
    Did your text give you an answer to this question? Was my answer not correct?

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    Reiny
  9. I just noticed that your same question was properly answered for you at
    https://www.jiskha.com/questions/1820564/a-farmer-finds-that-the-weights-of-sheep-on-his-farm-have-a-normal-distribution-with-mean
    by two capable tutors.
    As was pointed out at the end of these replies, there is no need to mess around with
    interpolation between values not given by tables.
    Tables are a thing of the past and the webpage that both oobleck and I gave you
    is extremely precise, and far superior to any tables.
    Btw, my answer is correct.

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    Reiny
  10. You didn't use continuity corrections and my text didn't gave correct answer.It gave 0.13128*250.

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  11. I got answer 32.82 people.While rounding off,will it be 32 or 33?

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  12. If its 32 then the answer is correct.Please explain how you round off people?

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  13. This is getting rather tiresome.

    Why are you multiplying 0.13128*250 ?
    when you were told the correct answer would be .1222*250 = 30.5

    and why are you talking about people, when the question dealt with SHEEP
    Of course you would round the 30.5 sheept to 31, geessshh

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    Reiny
  14. So the conclusion is not to use continuity correction.Am i right? Yeah, that was sheep not men.Sorry for that.

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