**Problem Statement:**Three different roads feed into a freeway entrance. Over an hour’s time, the number of cars entering the freeway for each road is a random variable (RV) with the expected value and standard deviation provided below:| Road | Expected Value | Standard Deviation ||--------|----------------|--------------------|| Road 1 | 180 | 36 || Road 2 | 900 | 22 || Road 3 | 500 | 15 |**Questions:**a) What is the expected number of cars entering the freeway over an hour?b) What is the standard deviation of the number of cars entering the freeway?**Solution:**a) The expected number of cars is the sum of the expected values from all roads:\[\text{Expected number of cars} = 180 + 900 + 500 = 1580\]b) The standard deviation of the total number of cars is calculated using the formula for the sum of independent random variables:\[\text{Standard deviation} = \sqrt{36^2 + 22^2 + 15^2} = \sqrt{1296 + 484 + 225} = \sqrt{2005} \approx 44.8\]An additional calculation shows a total variance of approximately 33,780 (shown in the work as a verification step).

Given data Road 1 Road 2 Road 3 Expected value 180 900 500 standard deviation 36 22 15

Answered: 52 3. Three different roads feed into a…

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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Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 8 million dollars and a standard deviation of 1.3 million dollars. One health care information systems company considers a quarter a "fallure" if its sales level that quarter is in the bottom 10% of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your Intermediate computations to at least four decimal places. Round your answer to one decimal place. million dollars X S Save For Later Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use 4 O * Check tab esc ! 1 ← 9. a @ 2 → W S # N = 3 C e $ 4 d r % 5 f acer Oll A t 6 g O. & 7 y h * u 8 j ( 1 9 k m 0 O P 1 M Submit Assignment Privacy Center Accessibility 10:12 backspace { 1 8民口團 11 D ?
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