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.

Question

Larry Mata

Business

2 October, 07:13

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.

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Answers (1)

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Fernando Doyle · Answer 1

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.