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    Calculating mean and standard deviation in the given case

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    A candy company claims that 17% of its plain candies are orange, and a sample of 100 such candies is randomly selected.

    a. Find the mean and standard deviation for the number of orange candies in such groups of 100.

    b. A random sample of 100 candies contains 5 orange candies. Is this result unusual? Does it seem that the claimed rate of 17% is wrong? Choose one from below

    1. Yes, because 5 is below the minimum usual value. Thus, the claimed rate of 17% is probably wrong.
    2. Yes, because 5 is greater than the maximum usual value. Thus, the claimed rate of 17% is not necessarily wrong.
    3. Yes, because 5 is within the range of usual values. Thus, the claimed rate of 17% is probably wrong.
    4. No, because 5 is within the range of usual values. Thus, the claimed rate of 17% is not necessarily wrong.

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    Solution Preview

    a. Find the mean and standard deviation for the number of orange candies in such groups of 100.
    Number of observations=n=100
    Probability of being orange=p=17%=0.17
    q=1-p=1-0.17=0.83

    Mean=np=100*.17=17
    Standard deviation=npq=100*0.17*0.83=14.11

    b. A ...

    Solution Summary

    Solution describes the steps to calculate mean and standard deviation in the given case.

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