Joe found an old copy of the Guinness Book of World Records. It stated that ther

Question

Joe found an old copy of the Guinness Book of World Records. It stated that there are on average 138 marriage licenses issued in Las Vegas per day in 2005 during the open hours of the licensing office. The licensing office is open from 9:00 am to 9:00 pm. Assume that licenses are independently issued. Let M be the number of marriage licenses in an hour on a day in 2005. What are the distribution, parameter(s), and support of M? What is the average and standard deviation of the number of marriage licenses issued in one hour? What is the probability that between 10 and 12 (inclusive) marriage licenses will be issued in an hour? One of the clerks has been tracking the licenses issued for every one hour increment a particular day. What is the probability that between 10 and 12 (inclusive) marriage licenses will be issued in 6 of those one-hour increments. State the distribution and parameter(s) you are using. What is the probability that the 4th hour that the license office is open, is the first one with between 10 and 12 (inclusive) marriage licenses issued? a) b) c) d) e)

Explanation / Answer

(e) Here first we have to find the expected number of marriage licenses issued in one hour = 138/12 = 11.5

here if X is the number of marriage occured in the given hour.

Pr(X = 10,11 & 12 ) = POISSON (X = 10 ; 11.5) + POISSON (X = 11; 11.5) + POISSON (X = 12; 11.5)

= 0.11294 + 0.11807 + 0.11315 = 0.3442

so as the question asked that 4th hour is the first one in which 10 to 12 marriage licenses issued.

so Pr(4 th one is in between 10 and 12 marriage licenses) = Pr(initial three are not like that) * Pr(fourth hour issue 10 to 12 marriage licences)

= (1- 0.3442)3 * 0.3442 = 0.0971

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