Recently, the federal government claimed that the state of Alaska had overpaid 20% of the Medicare recipients in the state.
The director of the Alaska Department of Health and Social Services planned to check this claim by selecting a random sample of 250 recipients of Medicare checks in the state and determining the number of overpaid cases in the sample.
Assuming the federal government's claim is correct, what is the probability that less than 15% of the people in the sample will be found to have been overpaid?