A traffic engineer reports that during the Spring Break in Miami Beach, 30% of t

Question

A traffic engineer reports that during the Spring Break in Miami Beach, 30% of the cars on the roads are from out-of-state, that is they have out-of-state license plates. Suppose during the Spring Break a traffic engineer randomly selects 10 cars from the Miami Beach for inspections find the probability that more than half of the selected cars are from out-of-state. [ Include the name of the probability model that you are using for this part.] Work: Suppose during the Spring Break another traffic engineer randomly select cars from the Miami Beach, one at a time, for inspections until she finds the third out-of state car. Find the probability that third out-of-car will be found at the 6th inspection. [ Include the name of the probability model that you are using for this part.] Work:

Explanation / Answer

This follows binomial distribution, with probability of success, p=0.3 and number of trials, n=10, r, the specific number of succeses in n trials is 5 or more.

Substitute values in formula, P(x=r)=nCr(p)^r(q)^n-r

P(x>=5)=1-P(x<5)=1-[P(x=0)+(x=1)+(x=2)+(x=3)+(x=4)]1-[0.028+0.121+0.233+0.267+0.2]=0.150

The second question follows negative binomial, Use following formula.

P(x,r,p)=x-1Cr-1(p)^r(1-p)^x-r

P(6,3,0.3)=5C2(0.3)^3(0.7)^3=0.093

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