Question

g. a second stage smog device has been installed on 50 different industry firms in los angeles. an inspector plans to visit 10 randomly selected industrial firms to check the device for violations. assume that 15 industrial firms violate smog regulations. what is the probability that 5 or less of the inspected firms will result smog violation

Answer 1

The probability that 5 or less of the inspected firms that will result smog volation is 0.944.

Given that among 50 different industrial firms, 15 violate smog regulations and the sample size be 10.

We are required to find the probability that 5 or less of the inspected firms that will result smog violation.

Probability is basically the calculation of likeliness of happening an event among all the events possible. It lies between 0 and 1.

Probability=Number of items/ Total items.

Probability that the firm violates the regulations if 1 industry is chosen from 50 industrial firms=15/50=0.3

Probability that 5 or less of the inspected firms will result somg violations among 10 industrial firms=$10C_{0}(0.3)^{0} (0.7)^{10}+ 10C_{1}(0.3)^{1} (0.7)^{9}+10C_{2}(0.3)^{2} (0.7)^{7}+10C_{3}(0.3)^{3} (0.7)^{7}+10C_{4}(0.3)^{4} (0.7)^{6}+10C_{5}(0.3)^{5} (0.7)^{5}$

=0.028+10*0.3*0.04+45*0.09*0.057+120*0.027*0.082+

210*0.0081*0.117+252*0.00243*0.16807

=0.028+0.12+0.23+0.265+0.199+0.102

=0.944

Hence the probability that 5 or less of the inspected firms that will result smog volation is 0.944.

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