Question

Part e) only

There are several scenarios described below. For each of them, do the following (note: R.V. means random 1. variable) (1) Define the R.V.that means something like, "Let X be the number of people who.... (2) Define the distribution and parameter(s) of the R.V (3) Give the support of the R.V. (4) Write the probability statement related to the information being sought. Do NOT calculate the probability. The city of Townsville has many potholes to fill. On the Main Street there are on average 3 potholes per half- mile of road. You want to find out the probability that there are 5 or 6 potholes in a particular one-mile a) Stretch of road. b) ry store yeu are about to choose a check-out lane, You have kept track of how often you choose At the groce the fastest lane when shopping. You calculate that you choose the fastest lane 18% of the time. You want to know the probability that on your shopping trip today you choose the fastest check-out lane. c) Maggie has a marble collection. In her collection jar are 45 marbles 15 are Aggies, 12 are Cats' Eyes, and the rest are Steelies. She randomly picks 8 marbles from the jar. She wants to know the probability that the she has chosen at least two Aggies when a certain traffic light turns yellow, 22% of the drivers try to make it through the intersection before the light turns red. A traffic cop is parked nearby and is monitoring the vehicles going through the light. He wants to know the probability that it will take at least 5 light changes until a driver tries to get through the light on the yellow. d) e) Fluxo manufacturing company makes parts for industrial furnaces. Approximately 1.2% of the parts it makes are defective. We are interested in calculating the probability that the third defective part is the 200th one sampled

Answer 1

a) This is an example of Poisson distribution.

average number of potholes in one mile stretch of road = 2* 3=6

Parameter $\lambda =6$

c) This is an example of binomial distribution, with

Parameters:probability of success ( Aggei's marbel ) p = 15/45=0.33

Total number of trials n=8

$P(X\leq 2)=\sum_{x=0}^{2}b(x,0.33,8)$

d) This is an example of geometric distribution

with parameter: the probability of success that the driver tries to make it through the intersection : p =0.22

We have to find the probability that it will take 5 trials (or light change ) until a driver tries  to make it through the intersection