Question

Explain why it would not be unusual to observe an individual who earns more than​ $100,000, but it would be highly unusual to observe a sample mean income of more than​ $100,000 for a random sample size of 100 people.

Answer 1

Answer:

Because about 10% are expected to earn $100,000

Explanation:

For a population with normal distribution N(74550, 19872), the probability of an individual getting a salary of more than 100000 is 0.1001, or about 10% are expected in this range. For sample mean based on size 100, the average distribution is N(74550, 19872/\sqrt{100}) = N(74550,1987.2) and the probability of the sample average exceeding 100000 is almost 0.