A) During his office-hour every Tuesday, Professor Chelst receives on average 2

Question

A) During his office-hour every Tuesday, Professor Chelst receives on average 2 students per hour, the students arrive according to Poisson distribution. If a random office hour lasts 1.5 hours, what is the probability that he receives more than 2 students?

B) The number of errors found in each chapter of a book is distributed according to a Poisson distribution with variance of 20. If each chapter of the book has exactly 40 pages, calculate the probability that we find at most 1 error in a randomly selected page.

Explanation / Answer

a)

There are 2 students/1hr, hence, 3 students/1.5 hr.

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    3      
          
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   2   ) =    0.423190081
          
Thus, the probability of at least   3   successes is  
          
P(more than   2   ) =    0.576809919 [ANSWER]

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