About 30% of new single-family homes completed in the United States during 2004 were heated with electricity. For a randomly selected sample of 25 new single-family homes completed during that year and the discrete random variable, 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.