Question 6: Match the descriptions below to the most appropriate of the six fami

Question

Question 6: Match the descriptions below to the most appropriate of the six families of distributions. Binomial Hypergeometric Gamma Poisson Negative binomial Normal (a) (5 pts) Let Xthe 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 Xthe 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 t 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 pouring the kibble, let Xthe 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) normal : weight is a continuous variable

(b) binomial: number of trials finite (3) , probability of choosing squeak toy constant

(c) negative binomial: number of failures before third success

(d) Poisson : number of trials large

(e) hypergeometric : out of N kibble , M is put in the basket and N-M is eaten

(f) gamma : elapse time

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