Medicare Hospital InsuranceThe average yearly Medicare Hospital Insurance benefit per person was$4064in a recent year. Suppose the benefits are normally distributed with a standard deviation of$460.Round the final answers to at least four decimal places and intermediatez-value calculations to two decimal places.

Part 1 of 2

Find the probability that the mean benefit for a random sample of

27patients is less than$3850

P(X < 3850) = ^{x is x bar}

Part 2 of 2

Find the probability that the mean benefit for a random sample of27patients is more than$4140.

P(x > 4140) ^{x is x bar}