Discrete Distributions Lab Exercises: Problem 1 Previous Problem Problem List Ne

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Discrete Distributions Lab Exercises: Problem 1 Previous Problem Problem List Next Problem (1 point) A local outfitter has thirty-two kayaks for weekend rental. On any given weekend, outfitter takes 40 reservations for the 32 kayaks, as he experiences "no-shows- those people with reservations who do not pick up the kayak. He estimates the probability of any reservation being a no-show is 0.30. As a result, the outfitter faces the possibility of "overbooking. Any person making a reservation who finds himself or herself without a kayak is provided with a free rental the following weekend- a policy that the outfitter clearly states when a reservation is made. (There are no guarantees, so pick up your reserved kayak early) What probability distribution will model this situation best? lE If rounding use at least four digits Part (a) What is the probability the outflitter rents only 25 kayaks on a given weekend? after the decimal in your answer) Pakt (b) During a fully booked weekend what is the probability that every person showing up to pick up his or her reserved kayak will have a kayak for the weekend? 1 (If rounding use at least four digits after the decimal in your answer) Part (c) During a fully booked weekend what is the probability that the outfitter overbooks? digits after the decimal in your answer Part (d) During a fully booked weekend how many kayaks should the outitter expect to rent on the weekend? lE If rounding use at least four lE If rounding use at least four digits after the decimal in your answer) Standard deviation? (If rounding use at least four digits after the decimal in your answer) Prevlew My Answers Submit Answens

Explanation / Answer

(a) A binomial distriubtion will suit this situation best and parameters n = sample size is given and p = probability of success is also given.

(b) Here for this binomial distribution

n = 40

p = 0.70 (for any person who did reservation had showed himself.

so Pr( X = 25 ) = BIN(X = 25 ; 40 ; 0.7)

by binomial calculator

Pr( X = 25 ) = BIN(X = 25 ; 40 ; 0.7) = 0.0774

(b) For a fully booked weekend that means all 40 seats were booked, now we have to find the probability that everybody who shpw up will get his kayak.

So, that means

Pr(X <= 32 ) = BIN(X <=32; 40; 0.7)

by binomial table

Pr(X <= 32 ) = BIN(X <=32; 40; 0.7) = 0.9447

Part(c) Outfitter Overbooks probabiity = Pr(X > 32 ; 40 ; 0.7) = 1 - 0.9447 = 0.0553

Part(d) Expected rented Kayaks = 40 * 0.7 = 28

Stanadard deviation = sqrt [40 * 0.7 * 0.3] = 2.8983

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