Consider a binomial experiment with n trials and probability of success p. If we assign a 0 to each failure and a 1 to each success, then the binomial random variable can be defined as a sum. By the...

Consider a binomial experiment with n trials and probability of success p. If we assign a 0 to each failure and a 1 to each success, then the binomial random variable can be defined as a sum. By the central limit theorem, as n increases the distribution of X (the sum) approaches a normal distribution with mean np and variance np(1 2 p). Suppose X is a binomial random variable with n = 30 and probability of success p = 0.5.

A hardware store has 20 interior plantation shutter sets in stock. The width (in inches) of each set is given in the table below.

a. Find the (population) mean width of the 20 shutters.

b. Use technology to generate at least 100 random samples of size five (without replacement). Find the sample mean width for each sample.

c. Construct a histogram of the sample means found in part (a). Describe the distribution.