Question

According to the M&M® website, the average percentage of brown M&M® candies in a package of milk chocolate M&Ms is 12%. (This percentage varies, however, among the different types of packaged M&Ms.) Suppose you randomly select a package of milk chocolate M&Ms that contains 60 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 60 candies?

i. The distribution is approximated by a normal distribution with mean 12 and standard deviation 0.0420.

ii. The distribution is approximated by a normal distribution with mean 7.2 and standard deviation 720.

iii. The distribution is approximated by a normal distribution with mean 0.12 and standard deviation 0.88. T

iv. The distribution is binomial and cannot be approximated.

v. The distribution is approximated by a normal distribution with mean 0.12 and standard deviation 0.0420.

(b) What is the probability that the sample proportion of brown candies is less than 23%? (Round your answer to four decimal places.)

(c) What is the probability that the sample proportion exceeds 32%? (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.) lower limit upper limit

Answer 1

The sampling distribution of proportion has approximately normal distribution (shape is bell shaped)

a) The correct choice is:

v. The distribution is approximated by a normal distribution with mean 0.12 and standard deviation 0.0420.

b) The probability that the sample proportion of brown candies is less than 23% is

c)  The probability that the sample proportion exceeds 32% is

d) The 95% confidence interval is