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Math Help - Standard deviation and mean question

  1. #1
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    Standard deviation and mean question

    A citrus farmer has determined that the diameters of its grapefruits are normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches.

    Is the answer of 4.2 correct?
    c. The farmer packs its largest grapefruits in special packages called the super pack. If 5 percent of all their grapefruits are packed as super packs, what is the smallest diameter of the grapefruits that are included\

    4.2


    I can't seem to find the formula for this problem.
    d. In this year’s harvest, there were 111,500 grapefruits that had a diameter over 5.01 inches. How many grapefruits has the grower harvested this year __________




    Please let me know if you can please help.

    Thank you
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  2. #2
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    Quote Originally Posted by desire150 View Post
    A citrus farmer has determined that the diameters of its grapefruits are normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches.

    Is the answer of 4.2 correct?
    c. The farmer packs its largest grapefruits in special packages called the super pack. If 5 percent of all their grapefruits are packed as super packs, what is the smallest diameter of the grapefruits that are included\

    4.2


    I can't seem to find the formula for this problem.
    d. In this year’s harvest, there were 111,500 grapefruits that had a diameter over 5.01 inches. How many grapefruits has the grower harvested this year __________




    Please let me know if you can please help.

    Thank you
    (c) If the mean is 4.5 then clearly Pr(X > 4.2) is much larger than 0.05 .... If you show all your working your mistakes can be pointed out to you.

    (d) Calculate p = Pr(X > 5.01). Then if Y is the random variable 'number of grapefruits with diameter larger than 5.01 inches' then Y ~ Binomial(n = 111,5000, p = as calculated). And you should know how to find the mean of Y.
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  3. #3
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    Dear Mr. Fantastic,
    I'm still confuse with the following two problems. I don't know where to start.
    (c) If the mean is 4.5 then clearly Pr(X > 4.2) is much larger than 0.05 .... If you show all your working your mistakes can be pointed out to you.



    (d) Calculate p = Pr(X > 5.01). Then if Y is the random variable 'number of grapefruits with diameter larger than 5.01 inches' then Y ~ Binomial(n = 111,5000, p = as calculated). And you should know how to find the mean of Y.
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  4. #4
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    Quote Originally Posted by desire150 View Post
    Dear Mr. Fantastic,
    I'm still confuse with the following two problems. I don't know where to start.
    (c) If the mean is 4.5 then clearly Pr(X > 4.2) is much larger than 0.05 .... If you show all your working your mistakes can be pointed out to you.

    Mr F says: My request is very simple here. Show your working. Do you understand that Pr(X > mean) = 0.5 and since mean = 4.5 then Pr(X > 4.2) > 0.5 and so your answer is wrong.



    (d) Calculate p = Pr(X > 5.01). Then if Y is the random variable 'number of grapefruits with diameter larger than 5.01 inches' then Y ~ Binomial(n = 111,5000, p = as calculated). And you should know how to find the mean of Y.
    (d) Surely you've been taught how to calculate Pr(X > 5.01). Then use that value in the Binomial distribution I have already mentioned.

    Until you show your working (as I asked) and are specific in where you're stuck then this is all I can say.
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