According to a study published by the College Board, the mean living expense for

Question

According to a study published by the College Board, the mean living expense for college students annually is $23, 500. Suppose that the distribution of living expenses for these students is bell-shaped and that the standard deviation is $2, 500. i) What shape of the distribution is required for The Empirical Rule? ii). If John's annual living expense is $30,000. Calculate Z-score for this observation. Z = x - x/s iii) Is John's annual living expense outlier? Why? Give an interval within which about 68% of annual living expenses fall for these college students. Jimmy's annual living expense has a z-score of -2. What is his annual living expenses?

Explanation / Answer

i) Normal distribution is required for empirical rule.

ii) John's z score = (30000 - 23500)/2500 = 2.6

iii) Yes, John's living expense is outlier because it lies outside the usual range of 2 standard deviation from the mean.

iv) Interval in which about 68% of annual living expense falls

= Interval of one standard deviation from the mean [As per the empirical rule]

= (23500 - 2500, 23500 + 2500)

= (21000, 26000)

v) Jimmy's living expense = 23500 - 2(2500) = $18500

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