A particularly long traffic light at an intersection is green 20% of the time. A

Question

A particularly long traffic light at an intersection is green 20% of the time. A car approaches this intersection once each day. Let X represent the number of days the car encounters a green light. Assume that each day represents an independent trial: a)Find the probability that the light is green on exactly three days over a ten day period. b)Find the probability that the light is green on at least three days over a ten day period. c)Find the expected value of the number of days the car encounters a green light over a ten day period. d) Find the standard deviation of the number of days the car encounters a green light over a ten day period.

Explanation / Answer

a)P(X=3)=(10C3)(0.2^3)(0.8^7) b)1-P(X=0)-P(X=1)-P(X=2)=1-(10C0)(0.2^0)(0.8^10)-(10C1)(0.2^1)(0.8^9)-(10C2)(0.2^2)(0.8^8) c) as expectation of a binomial (n,p) random variable is np here it is =10*0.2=2 d)as standard deviation of a binomial (n,p) random variable is (npq)^.5=1.6^0.5=1.2649

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