The net-worth of families in New Brunswick in thousand dollars has a mean of 220

Question

The net-worth of families in New Brunswick in thousand dollars has a mean of 220 with a standard deviation of 40. A sample of families in New Brunswick is interviewed and the sample mean net-worth is computed. a) What would you expect the shape of the distribution of the net-worth of families in New Brunswick to look like? b) Assuming a large enough sample size, what would you expect the shape of the sampling distribution for the sample mean to look like? c) What would be the mean of this sampling distribution? d) If the sample size is 50, what would be the standard deviation of this sampling distribution? e) If the sample size is 100, what would be the standard deviation of this sampling distribution?

Explanation / Answer

a) the shape of distribution would be approximately normal, though we can only asssume till we do not know other charecteristics.

b) as sample size is large enough we can expect from central limit theorum that shape of sampling distribution of mean will be approximately normal regardless of shape of population distribution

c) mean of sampling distribution =220

d) std deviation of sampling distribution=std deviation of population/(n)1/2 =40/(50)1/2 =5.6569

e) for n=100; std deviation of sampling distribution=std deviation of population/(n)1/2 =4

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