According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags of Skittles,

Question

According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags of Skittles, what is the probability that the proportion in our sample of red candies will be less than 20%

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Gianna 3 days 2021-10-09T20:37:39+00:00 1 Answer 0

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    2021-10-09T20:38:54+00:00

    Answer:

    Probability that the proportion in our sample of red candies will be less than 20% is 0.5 .

    Step-by-step explanation:

    We are given that 20% of the candy produced are red. A random sample of 100 bags of Skittles is taken.

    The distribution we can use here is;

                   \frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } ~ N(0,1)

    where, p = 0.20 and n = 100

    Let \hat p = proportion of red candies in our sample

    So, P(\hat p < 0.20) = P(\frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } < \frac{0.20 - 0.20}{\sqrt{\frac{0.2 (1- 0.2)}{100} } } ) = P(Z < 0) = 0.5

    Therefore, probability that the proportion in our sample of red candies will be less than 20% is 0.5 .

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