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Question

dill Connect Ma X connectmath.com/alekscgitsAslx1o u-lgNslkr78P3jH-IQiucBg67JjQRhoz9hcTVPOHqG1jTqadFYH12 nect IMATH losted by ALEXS Corp Copy of Homework 6.2 PreviouS 23 145 Next Question 5 of 6 (1 point) 6.2 Section Exercise 18 (calc) The average charitable contribution itemized per income tax return in Pennsyvania is $792. Suppose that the distribution of contributions is normal with a standard deviation of $92 Find the limits for the middle 40% of contributions. Use a graphing calculator and round the answers to two decimal places. Source: IRS, Statistics of Income Bulletin. The limits for the middle 40% of contributions are $1 741-03 | and ??

Explanation / Answer

To find the middle 40% of contributions we need to find 30th percentile and 70th percentile

Let 30th percentile be denoted as 'P30'

Let 70th percentile be denoted as 'P70'

We have,

P(X < P30 ) = 0.30

P( (X - mean) / SD < (P30 - mean ) / SD ) = 0.30

P( Z < (P30 - 792) / 92 ) = 0.30

Using Standard normal tables,

(P30 - 792 ) / 92 = - 0.5244

P30 = 743.76

P(X < P70 ) = 0.70

P( (X - mean) / SD < (P70 - mean ) / SD ) = 0.70

P( Z < (P70 - 792) / 92 ) = 0.70

Using Standard normal tables,

(P70 - 792 ) / 92 = 0.5244

P30 = 840.24

The limits for the middle 40% of contribution are $ 743.76 and $ 840.24

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