A second-stage smog alert has been called in a certain area of Los Angeles Count
ID: 3306146 • Letter: A
Question
A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 59 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations.
a. Suppose 16 of the firms are actually violating at least one regulation. What is the probability that the inspector will find 2 firms in violation of at least one regulation?
______________ (round to 3 decimal places)
b. If there are 590 firms in the area, of which 160 are in violation, find the probability of part a using a simpler pmf.
_____________(round to 3 decimal places)
Explanation / Answer
a. The probability that a firm violates the regulation = 16/59 = 0.27
Probability that a firm does not violate the regulation = 1 - 0.27 = 0.73
The two firms that violate the regulation can come in 10C2 = 45 ways.
=> Probability that two given firms violate the regulation = 0.27*0.27 = 0.0789
Probability that the other eight firms do not violate the regulation = 0.738 = 0.0806
The probability that exactly two firms will violate the regulation = 45 * 0.0789 * 0.0806 = 0.286.
b. pmf is 10C2 * p2 (1-p)8
p = 160/590 = 0.2711 1 - p = 0.7289
=> Probability = 10C2 * (0.2711)2 * (0.7289)8
= 0.237.
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