a. Itemized Charitable Contributions - Theaverage charitable contribution itemiz

Question

a. Itemized Charitable Contributions - Theaverage charitable contribution itemized per income tax return inPennsylvania is $792. Suppose that the distribution ofcontributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions. b. Reading Improvement Program - To help studentsimprove their reading, a school district decides to implement areading program. It is to be administered to the bottom 5% ofthe students in the district, based on the scores on a readingachievement exam. If the average score for the students inthe district is 122.6, find the cutoff score that will make astudent eligible for the program. The standard deviation is18. Assume the variable is normally distributed. a. Itemized Charitable Contributions - Theaverage charitable contribution itemized per income tax return inPennsylvania is $792. Suppose that the distribution ofcontributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions. b. Reading Improvement Program - To help studentsimprove their reading, a school district decides to implement areading program. It is to be administered to the bottom 5% ofthe students in the district, based on the scores on a readingachievement exam. If the average score for the students inthe district is 122.6, find the cutoff score that will make astudent eligible for the program. The standard deviation is18. Assume the variable is normally distributed.

Explanation / Answer

(a) Given =0.5, |Z(0.25)|=0.68 (check normal table) SO ± (z*) --> 792 ± (0.68 * 103) --> ( 721.96, 862.04) (b) Z score = (X - 122.6)/18 = -1.65 -1.65 is the value of a standard normal z table where the area(probability) to the left of the value is 0.05 (5%). Solve for X = 92.9 So any score 92.9 will fall in this 5%.

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