More than 50 million guests stay at bed and breakfasts BBs e

More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed and Breakfast Inns of North America, which averages five visitors per minute, enables many B&Bs to attract guests.

a. Compute the probability of no website visitors in a one-minute period.
b. Compute the probability of two or more website visitors in a one-minute period.
c. Compute the probability of one or more website visitors in a 30-second period.
d. Compute the probability of five or more website visitors in a one-minute period.

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    5      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.006737947 [ANSWER]

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B)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    5      
          
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.040427682
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.959572318 [ANSWER]

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c)

In 30 s, the average is 5/2 = 2.5 visitors.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    2.5      
          
x = our critical value of successes =    1      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   0   ) =    0.082084999
          
Thus, the probability of at least   1   successes is  
          
P(at least   1   ) =    0.917915001 [ANSWER]

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d)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    5      
          
x = our critical value of successes =    5      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   4   ) =    0.440493285
          
Thus, the probability of at least   5   successes is  
          
P(at least   5   ) =    0.559506715 [ANSWER]