Question 6 Match the descriptions below to the most appropriate of the six famil

Question

Question 6 Match the descriptions below to the most appropriate of the six families of distributions. Binomial Gamma Poisson Negative binomial Normal (a) (5 pts) Let X = the total weight of the 400 pieces of kibble that I fed Peter for breakfast this morning. (b) (5 pts) There are 4 squeak toys and 3 rope toys Peter's toy bin. Peter reaches in and grabs 3 toys at random (that's how many he can fit in his mouth at once)Let X = the number of squeak toys that end up in his mouth. (c) (5 pts) Peter sits on by a bench downtown and, independently, decides to lick (with proba- bility p) or not lick (with probability 1 - p) the people who pass by. Let X the number of people who walk buy until the third one to get licked. (d) (5 pts) Out of the next 20 people who pass by on the sidewalk, let X = the number of them that get licked. (e) (5 pts) When I buy a new bag of dog kibble, I pour it from the bag into a plastic storage bin. Each piece has some small probability (independently) of bouncing out of the bin and onto the floor (and hence immediately being eaten). Let X the number of pieces of kibble that Peter gets to eat while I'm pouring it into the bin. (f) (5 pts) Once I start pouringthekibble, let X = the length of time that will elapse until five pieces of kibble find their way onto the floor and into Peter's belly.

Explanation / Answer

a) Weight is generally normally distributed.Hence,the total weight distribution will be NORMAL.

b)Here,Peter grabs random ly 3 toys from a collection of 7 toys and X is number of squak toys grabbed by him.So,it is basically a setup of hypergeometric deistribution.Here 4 toys are of one kind and 4 toys are of another knind and i want to see probability of number of toys of one kind from collection total of 3 toys chosen .So,it is HYPERGEOMETRIC.

c)When Peter licks the 3rd person,the success occurs.For each people,he chooses to lick or not to lick independently with probabilities being same for each licking.So,X is the number of person Peter is not licking ie failure to lick. So,it is NEGATIVE BINOMIAL distribution.(no. of tries untill 3 successes{licking means success})

d) X is no. of persons to get licked out of 20 persons.Each person gets(success) or does not get(failure) licked independently.Hence,this is clearly a Binomial DISTRIBUTION.

e)Among n kibbles,one kibble bounce out of the bin with very small probability suc that average number of bins bounced out from the bins are more or less constant.So,comparing,this is a case of POISSON DISTRIBUTION.

f)We have to find the waiting time until 5 pieces of kibbles enters Peters mouth.By result,waiting time follows gamma or exponential.Hence,GAMMA is the answer.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.