(Solution) - About 40 of new single family homes completed in the United -(2025 Original AI-Free Solution)

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About 40% of new single-family homes completed in the United States during 2007 were heated with electricity. For a randomly selected sample of 20 new singlefamily homes completed during that year and the discrete random variable, x = the number of homes in this group heated with electricity:
a. Calculate the mean and standard deviation of the binomial distribution.
b. Using the binomial distribution tables, determine the probability that x will be exactly 8 homes heated with electricity.
c. Using the binomial distribution tables, determine the probability that x will be at least 6 but no more than 9 homes.
d. Repeat part (b), using the normal approximation to the binomial distribution.
e. Repeat part (c), using the normal approximation to the binomial distribution.