Twinkies are an American snack cake that have been sold for over 83 years. Hostess Brand, the distributing company, claims that 15% of all households in the U.S. buy Twinkies regularly.

1.) A random sample of 10 U.S. households will be selected. Find the probability that the number of households in the sample who buy Twinkies regularly will be within one standard deviation of the mean number of households.

2.)Suppose that the random sample of 10 U.S. households resulted in all 10 households buy Twinkies regularly. Does this result make you doubt the claim made by Hostess Brand, the distributing company? Provide numerical support.