### Problem 2: Charitable Contributions in Pennsylvania**Problem Description:**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 $103. Find the limits for the middle 50% of contributions.**Solution Outline:**1. **Identify the Mean and Standard Deviation:** - Mean ($\mu$): $792 - Standard Deviation ($\sigma$): $1032. **Understanding the Middle 50%:** - The middle 50% of a normal distribution is centered around the mean, covering from the 25th percentile to the 75th percentile.3. **Find the Z-scores for the 25th and 75th Percentiles:** - The Z-score for the 25th percentile is approximately -0.675. - The Z-score for the 75th percentile is approximately +0.675.4. **Convert Z-scores to Contribution Values:** - Use the Z-score formula: $X = \mu + Z\sigma$ - For 25th percentile: $X_{25} = 792 + (-0.675)(103) \approx 723.45$ - For 75th percentile: $X_{75} = 792 + (0.675)(103) \approx 860.55$**Conclusion:**The limits for the middle 50% of charitable contributions itemized per income tax return in Pennsylvania are approximately $723.45 and $860.55.

2) Given, The average charitable contribution itemized per income tax return in Pennsylvania is…

Answered: 2. The average charitable contribution…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. 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.