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Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s).

Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 33E: Sick leave probability that a given worker at Dyno Nutrition Will call in sick on a Monday is 004....
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Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
Transcribed Image Text:Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
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