Suppose the distribution of family incomes of all the US households is positivel

Question

Suppose the distribution of family incomes of all the US households is positively skewed with mean 71,000 and standard deviation 15,000.
a. I randomly pick 2000 families in the US and make a histogram of the incomes of these 2000 families. What would the histogram look like?
ex. positively skewed, negatively skewed, normal, approximately normal
b.If I randomly pick a family in the US, what is the probability that this family’s income is below 70,000?
ex. 7%, 47.21%, 2.79%, there is not enough information
c. If I draw numerous samples from the US and each sample has 2000 families. For each sample I calculate the average income of the families in that particular sample. What would the sampling distribution of average family incomes look like?
ex. positively skewed, negatively skewed, normal, approximately normal
d. Based on the central limit theorem, what is the probability that the average income of some 2000 families is below 70,000?

Explanation / Answer

a)

positively skewed

b )

there is not enough information

c)

approximately normal

due to central limit theorem

d) mean = 71000 , sd = 15000, n = 2000

P(X < 70000)

Z =(Xbar - 71000)/(15000/sqrt(2000)

P(X < 70000)

= P (Z<2.98)=0.0014

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