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A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 90 industrial firms. An Inspector will visit 30 randomly selected firms to check for vlolations of regulations. (a) If 36 of the firms are actually violating at least one regulation, what is th nmf of the number of firms visited by the inspector that are in violation of at least one regulation? O h(x; 30, 0.4) O nb(x; 30, 0.4) O h(x; 30, 36, 90) O b(x; 30, 0.4) O nb(x; 30, 36, 90) O b(x; 30, 36, 90) (b) If there are 900 firms in the area, of which 360 are in violation, approximate the pmf of part (a) by a simpler pmf. O h(x; 30, 360, 900) O nb(x; 30, 0.4) Ob(x; 30, 0.4) O nb(x; 30, 360, 900) O h(x; 30, 0.4) O b(x; 30, 360, 900) (c) For X - the number that are in violation among the 30 visited out of 900 firms, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b). (Round your answers to two decimal places.) Compute E(X) and V(X) for the exact pmf. E(X) - V(X) = Compute E(X) and V(X) for the approximating pmf. E(X) = V(X) -

A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 90 industrial firms. An Inspector will visit 30 randomly selected firms to check for vlolations of regulations. (a) If 36 of the firms are actually violating at least one regulation, what is th nmf of the number of firms visited by the inspector that are in violation of at least one regulation? O h(x; 30, 0.4) O nb(x; 30, 0.4) O h(x; 30, 36, 90) O b(x; 30, 0.4) O nb(x; 30, 36, 90) O b(x; 30, 36, 90) (b) If there are 900 firms in the area, of which 360 are in violation, approximate the pmf of part (a) by a simpler pmf. O h(x; 30, 360, 900) O nb(x; 30, 0.4) Ob(x; 30, 0.4) O nb(x; 30, 360, 900) O h(x; 30, 0.4) O b(x; 30, 360, 900) (c) For X - the number that are in violation among the 30 visited out of 900 firms, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b). (Round your answers to two decimal places.) Compute E(X) and V(X) for the exact pmf. E(X) - V(X) = Compute E(X) and V(X) for the approximating pmf. E(X) = V(X) -

MATLAB: An Introduction with Applications
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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**Smog Alert Inspection Analysis** A second-stage smog alert has been issued in a specific area of Los Angeles County, encompassing 90 industrial firms. An inspector will conduct visits to 30 randomly selected firms to assess compliance with regulations. 1. **Problem (a):** - **Question:** If 36 of the firms are actually in violation of at least one regulation, what is the probability mass function (PMF) of the number of firms visited by the inspector that are in violation? - **Options:** - \( \circ \) \( h(x; 30, 0, 4) \) - \( \bullet \) \( h(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 36, 90) \) 2. **Problem (b):** - **Question:** If there are 900 firms in the area, and 360 are in violation, approximate the PMF of part (a) using a simpler PMF. - **Options:** - \( \circ \) \( h(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \bullet \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \circ \) \( b(x; 30, 360, 900) \) 3. **Problem (c):** - **Task:** For \( X \) – the number of firms in violation among the 30 inspected out of 900 firms – compute the expected value \( E(X) \) and variance \( V(X) \) for both the exact PMF and the approximating PMF from part (b). (Round your answers to two decimal places.) - **Exact PMF:** - \( E(X) = \_\_\_\_ \) -
Transcribed Image Text:**Smog Alert Inspection Analysis** A second-stage smog alert has been issued in a specific area of Los Angeles County, encompassing 90 industrial firms. An inspector will conduct visits to 30 randomly selected firms to assess compliance with regulations. 1. **Problem (a):** - **Question:** If 36 of the firms are actually in violation of at least one regulation, what is the probability mass function (PMF) of the number of firms visited by the inspector that are in violation? - **Options:** - \( \circ \) \( h(x; 30, 0, 4) \) - \( \bullet \) \( h(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 36, 90) \) - \( \circ \) \( b(x; 30, 36, 90) \) 2. **Problem (b):** - **Question:** If there are 900 firms in the area, and 360 are in violation, approximate the PMF of part (a) using a simpler PMF. - **Options:** - \( \circ \) \( h(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \bullet \) \( b(x; 30, 0.4) \) - \( \circ \) \( nb(x; 30, 360, 900) \) - \( \circ \) \( h(x; 30, 0.4) \) - \( \circ \) \( b(x; 30, 360, 900) \) 3. **Problem (c):** - **Task:** For \( X \) – the number of firms in violation among the 30 inspected out of 900 firms – compute the expected value \( E(X) \) and variance \( V(X) \) for both the exact PMF and the approximating PMF from part (b). (Round your answers to two decimal places.) - **Exact PMF:** - \( E(X) = \_\_\_\_ \) -
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