The mean household income in a country in a recent year was about $77 comma 044 and the standard deviation was about $84 comma 000. (The median income was $58 comma 423.) a) If a Normal model was used for these incomes, what would be the household income of the top 1%? b) How confident should one be in the answer in part a? c) Why might the Normal model not be a good one for incomes?

a) Income of $272,428 or more would be top 1%.

b) Skewed right

c) Not always normally distributed

Explanation:

We are given the following information in the question:

Mean, μ = $77,044

Standard Deviation, σ = $84,000

Median = $58,423

a) We follow a normal mode

Formula:

We have to find the value of x such that the probability is 0.01

P(X > x)  

Calculation the value from standard normal z table, we have,  

Thus, income of $272,428 or more would be top 1%.

b) We should not be confident as the median is not equal to the mean. Hence, it is not a normal distribution. It was just an assumption. Since the mean is greater than the median the distribution of income is skewed towards right.

c) Normal model not be a good one for incomes because the median may not always e equal to the mean and hence, they do not follow a normal distribution.

i believe it’s b because the rest don’t make sense

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