The average income of a country is known to be 10 000 with standard deviation 2500. A

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The average income of a country is known to be £10 000 with standard deviation £2500. A sample of 40 individuals is taken and their average income calculated.

(a) What is the probability distribution of this sample mean?

(b) What is the probability of the sample mean being over £10 500?

(c) What is the probability of the sample mean being below £8000?

(d) If the sample size were 10, why could you not use the same methods to find the answers to (a)–(c)?

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