A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 90 industrial firms. Aninspector will visit 20 randomly selected firms to check for violations of regulations.(a) If 27 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by theinspector that are in violation of at least one regulation?O h(x; 20, 0.3)O nb(x; 20, 0.3)О Бx; 20, 27, 90)О Бix; 20, 0.3)O h(x; 20, 27, 90)nb(x; 20, 27, 90)(b) If there are 900 firms in the area, of which 270 are in violation, approximate the pmf of part (a) by a simpler pmf.O b(x; 20, 0.3)O b(x; 20, 270, 900)O h(x; 20, 0.3)O h(x; 20, 270o, 900)O nb(x; 20, 0.3)O nb(x; 20, 270, 900)(c) For X = the number that are in violation among the 20 visited out of 900 firms, compute E(X) and V(X) both for theexact 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) =

Answered: A second-stage smog alert has been…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A study was conducted to determine whether a woman's risk of transmitting HIV to her unborn child is different for the younger vs. the older the child. A sample of 100 HIV- infected women who gave birth to two children found that, when only one of the two siblings had HIV, it occurred in 7 of the 100 older siblings and in 15 of the younger siblings, as shown in the table below. Younger sibling HIV? Yes No Yes 7 Older sibling HIV? No 15 76 (a) We are not interested in the case when both siblings are HIV positive or the case when both are not HIV positive. We are only interested in the two cases in which one sibling is HIV positive and the other is not (the 7 and 15). Test Ho: the probability of being HIV positive is the same for older siblings as it is for younger siblings along with the alternative HA: the probabilities are different. Use a = .10. (b) Test the hypothesis if HA is directional, that the younger sibling (15 in the table) is more likely than the older sibling to have HIV.…
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