Quiz 2

3. The mean household income in a country in a recent year was about ​$77,011 and the standard deviation was about ​$84,000. ​(The median income was ​$49, 711​.)

​a) If a Normal model was used for these​ incomes, what would be the household income of the top 2 ​%?

​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. The income would be _____ ​(Round to the nearest dollar as​ needed.)

b) Choose the correct answer below.

1. Not very​ confident, as people tend to​ over-exaggerate their earnings when reporting their income.
2. Very​ confident, as one would expect the top 2​% of household incomes to be close to the value in part a.
3. Very​ confident, as the​ mean, and not the​ median, was used to calculate the top 2​% of incomes.
4. Not very​ confident, as the standard deviation is larger than the​ mean, and subtracting one standard deviation from the mean results in nonsensical incomes.

c) Choose the correct answer below.

1. Since the median is much less than the mean and the standard deviation is greater than the​ mean, the distribution of incomes is likely left skewed. The Normal model is only appropriate for data which are unimodal and symmetric.
2. Since people tend to​ over-exaggerate their earnings when reporting their​ income, the reported mean and standard deviation may not be reliable.
3. It is likely that the data have more than one mode. The Normal model is only appropriate for data which are unimodal and symmetric.
4. Since the median is much less than the mean and the standard deviation is greater than the​ mean, the distribution of incomes is likely right skewed. The Normal model is only appropriate for data which are unimodal and symmetric.