4. There are several scenarios described below. For each of them, state the distribution and parameter(s) of the random variable. Write out the support. Write the probability statement related to the information being sought. Do NOT calculate the probability. ALSO give the mean and S.D. of them.

a) The city of Moonsville has many potholes to fill. On the Main Street there are 4 potholes per mile of road. You want to find out the probability that there are 5 or 6 potholes in a particular one-mile stretch of road. Let be the number of potholes in a particular two-mile stretch of road.

_____________ ,

Parameter = ___________________,

Support of = {_____________________},

(= 5 6) = __________________,

E[]= ________________, S.D.()= __________________.

b) At the supermarket you are about to choose a check-out lane. You have kept track of how often you choose the fastest lane when shopping. You calculate that you choose the fastest lane 20% of the time. You want to know the probability that on your shopping trip today you choose the fastest check-out lane. Let be whether you choose the fastest check-out lane or not.

_________________ ,

Parameter = ___________________,

Support of = {____________________} ,

( = 1)=____________________ ,

E[]= ________________, S.D.()= _________________.

c) When a certain traffic light turns yellow, 10% 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. Let be the number of light changes it will take until a driver tries to get through the light on the yellow.

_______________,

Parameter = _______________,

Support of = {__________________________} ,

( 5) = ______________________,

E[]= __________________, S.D.()=___________________ .

d) Sun manufacturing company makes parts for industrial furnaces. Approximately 1% of the parts it makes are defective. We are interested in calculating the probability that the third defective part is the 200th one sampled. Let be the number of parts sampled to find the third defective part.

________________,

Parameter = _____________________,

Support of = { _____________________} ,

(=200) = _____________________,

E[]= _____________________, S.D.()=_____________________ .