Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities. (a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?