### Designing Aircraft Seats for Male Passenger Hip Breadth**Objective:** Engineers seek to design seats in commercial aircraft that are sufficiently wide to fit 90% of all males. (Accommodating 100% of males would necessitate excessively wide seats and be prohibitively expensive.) The focus is on men whose hip breadths are normally distributed with a mean of 13.9 inches and a standard deviation of 0.8 inches. The task is to find P₉₀, the hip breadth that separates the smallest 90% from the largest 10%.#### Introduction**Normal Distribution Parameters:**- Mean (μ): 13.9 inches- Standard Deviation (σ): 0.8 inches**Goal:** Find the hip breadth (P₉₀) that separates the smallest 90% from the largest 10% of the distribution.#### Step-by-Step Process1. **Determine the Z-score:** Use technology to find the Z-score corresponding to the given area (90%). This is achieved through the Z-score table or statistical software/calculators.2. **Concept of the 90th Percentile:** - The 90th percentile, P₉₀, implies that 90% of the data falls below this value. - Mathematically, it means the area under the normal curve to the left of x is equal to 0.9000.**Graphical Representation:** - A bell curve (normal distribution) shows a shaded area of 0.90 on the left side. - There is a vertical line marking the mean (13.9 inches) and another at the value x, which signifies the 90th percentile.3. **Calculation:** - Use the Z-score formula:\[ x = \mu + (z \cdot \sigma) \] - Find z that corresponds to the shaded area of 0.9000. - For Z = 1.28 (rounded to two decimal places). **Conclusion:** By substituting the known values into the formula:\[ x = 13.9 + (1.28 \cdot 0.8) \]\[ x = 13.9 + 1.024 \]\[ x = 14.924 \]Thus, the hip breadth separating the smallest 90% from the largest 10% of men is approximately 14.

Let us suppose the required Z-score be z such that P(Z< z) =0.9000 Since, In the given problem,…

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 13.9 in. and a standard deviation of 0.8 in. Find Pao. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%.

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 13.9 in. and a standard deviation of 0.8 in. Find Pao. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%.

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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