1. Suppose the random variable X has a binomial distribution corresponding to n = 20 and p = 0.40. Use the Cumulative Binomial Probabilities table to calculate these probabilities. (Enter your answers to three decimal places.)

(a) P(X = 7)

(b) P(X 9)

2. A random sample of n observations is selected from a population with standard deviation = 1. Calculate the standard error of the mean (SE) for these values of n. (Round your answers to three decimal places.)

(a)n = 1SE =

(b)n = 2SE =

(c)n = 4SE =

(d)n = 9SE =

(e)n = 16SE =

(f)n = 25SE =

(g)n = 100SE =

3. 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 58 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 58 candies

--The distribution is approximated by a normal distribution with mean 7.0 and standard deviation 696.

--The distribution is approximated by a normal distribution with mean 0.12 and standard deviation 0.0427.

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

--The distribution is approximated by a normal distribution with mean 12 and standard deviation 0.0427.

The distribution is binomial and cannot be approximated.

(b) What is the probability that the sample proportion of brown candies is less than 18%? (Round your answer to four decimal places.) (c) What is the probability that the sample proportion exceeds 30%? (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

4. Random samples of size n were selected from populations with the means and variances given here. Find the mean and standard deviation of the sampling distribution of the sample mean in each case. (Round your answers to four decimal places.)

(a)n = 64, = 13, ² = 9==

(b)n = 100, = 9, ² = 4==

(c)n = 8, = 111, ² = 1==