The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation
Of $103. Find the limits for the middle 50% of contributions.
A) $723 and $861
B) $766 and $818
C) $741 and $844
D) $758 and $826

Question

Quizplus · Accepted Answer

The middle 50% of contributions corresponds to the interquartile range, which is between the 25th percentile (Q1) and the 75th percentile (Q3) in a normal distribution. For a normal distribution, these percentiles are approximately 0.675 standard deviations away from the mean in either direction. Therefore, we calculate the limits as follows: Lower limit = Mean - (0.675 * Standard Deviation) = $792 - (0.675 * $103) ≈ $723 Upper limit = Mean + (0.675 * Standard Deviation) = $792 + (0.675 * $103) ≈ $861

The Average Charitable Contribution Itemized Per Income Tax Return in Pennsylvania