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The income for the US has a normal distribution with a population mean of $50,000 and a population standard deviation of $4,000.

a. A random sample of 1600 people was taken. What is the probability that the mean income for that sample will be greater than $50,200?

b. A random sample of 400 people was taken. What is the probability that the mean income for that sample will be greater than $49,700?

c. A random sample of 100 people was taken. What is the probability that the mean income for that sample will be less than $49,000?

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