As part of an air-pollution survey, an inspector decides to examine the exhaust
ID: 3181654 • Letter: A
Question
As part of an air-pollution survey, an inspector decides to examine the exhaust of 5 of a company's 10 trucks. If 3 of the company's trucks emit excessive amounts of pollutants, 1.1a) what is the probability distribution of the number of trucks that emit excessive amounts of pollutants in the sample of 5? (Use a table that lists all the possible values and associated probabilities.) 1.1b) what is the expected number of trucks that emit excessive amounts of pollutants in the sample of 5? If the probability is 0.75 that an applicant for a driver's license will pass the road test on any given try. 1.2.a) what is the probability that an applicant will finally pass the test on the fourth try? 1.2.b) What is the expected number of tries in order to pass the test?Explanation / Answer
1.1) Here , X is random variable which represents which represents number of trucks that emits excessive amounts of pollutants in a sample of size n=5 & X ~ Binomial (n=5,p=3/10=0.3)
1.1a) Probability mass function of X is ,
P(X=x) =nCx px(1-p)n-x =5Cx 0.3x *0.75-x ; x=0,1,......,5
1.1b) Expected number of trucks that emits excessive amounts of pollutants in a sample of size n=5 is ,
E(X)=n*p=5*0.3=1.5
X P(X=x) 0 0.16807 1 0.36015 2 0.3087 3 0.1323 4 0.02835 5 0.00243Related Questions
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