**Educational Transcription and Analysis**### Problem 3A manufacturer produces one run of their tie-dyed cheescloth undershirts, with potential demand sizes of 5,000, 6,000, 8,000, or 10,000 shirts. The probability distribution for demand is provided in a table:| X | 5,000 | 6,000 | 8,000 | 10,000 ||---------|-------|-------|-------|--------|| P(X) | 0.3 | 0.4 | 0.2 | 0.1 |**a) Expected Profit Calculation**If the profit per undershirt is $2.75, find the expected weekly profit:Calculations:- Expected demand = (5,000 * 0.3) + (6,000 * 0.4) + (8,000 * 0.2) + (10,000 * 0.1) = 4,900- Expected Profit = 4,900 * $2.75 = $12,000- *Mistake noted in red: 3***b) Standard Deviation of Undershirts**To find standard deviation:- Use the formula: \[ \sigma = \sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)} \]- Here, $\mu = 4,900$, and the calculations yield a standard deviation of approximately 70.### Problem 4An automobile manufacturer purchases computer chips that have a 5% defect rate. Each car uses 12 chips selected independently.**a) Probability at Least 11 Chips Work Properly**Use the binomial probability formula:- \[ P(X \geq 11) = 1 - P(X \leq 10) = \sum_{k=0}^{10} \binom{12}{k}(0.05)^k(0.95)^{12-k} \]- Calculations show P(X = 12) and P(X = 11) are very low, with a high-level computation noted.**b) Mean and Standard Deviation of Defective Chips**- Mean ($M$) = n * p = 12 * 0.05 = 0.6- Standard Deviation (\(\

Answered: Image /qna-images/answer/70498880-d85d-4db4-a7e3-bf5ceec54599.jpg

Answered: market for the undershirts has held up…

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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