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An advertiser claims that the average percentage of brown M&M'S candies in a package of milk...

An advertiser claims that the average percentage of brown M&M'S candies in a package of milk chocolate M&M'S is 14%. Suppose you randomly select a package of milk chocolate M&M'S that contains 54 candies and determine the proportion of brown candies in the package.

(a) What is the approximate distribution of the sample proportion of brown candies in a package that contains 54 candies?

The distribution is approximated by a normal distribution with mean 0.14 and standard deviation 0.86.The distribution is approximated by a normal distribution with mean 14 and standard deviation 0.0472.    The distribution is approximated by a normal distribution with mean 7.6 and standard deviation 756.The distribution is binomial and cannot be approximated.The distribution is approximated by a normal distribution with mean 0.14 and standard deviation 0.0472.


(b) What is the probability that the sample percentage of brown candies is less than 20%? (Round your answer to four decimal places.)


(c) What is the probability that the sample percentage exceeds 33%? (Round your answer to four decimal places.)


(d) Within what range would you expect the sample proportion to lie about 95% of the time? (Round your answers to two decimal places.)

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