Information gathered by the Central Weather Office over a long period reveals th

Question

Information gathered by the Central Weather Office over a long period reveals that the number of severe snowstorms experienced by a large urban centre follows the Poisson law with an average of three such storms per year. What is the probability that the number of severe snowstorms next year will be smaller than four? Compute the probability that in a two-year period the urban centre will experience more than four but fewer than eight severe snowstorms. The digital cameras manufactured by Marvel cam come in either a 10 megapixel version or a 20 megapixel version. The owner of a camera store received a shipment of fifteen cameras from Marvel cam: six 10 megapixel and nine 20 megapixel cameras. An employee randomly selects five of these cameras and stores them behind the counter; he then places the remaining ten cameras in the storeroom. Let X denote the number of 10 megapixel cameras stored behind the counter. Compute the probability that X is larger than two. Write down t

Explanation / Answer

2. (A)

a)

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    3      
          
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.647231889
          
Which is also          
          
P(fewer than   4   ) =    0.647231889 [ANSWER]

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b)

Hence, in 2 years, the mean is 2 years*(3 per year) = 6.

The problem means from 5 to 7 inclusive, as 4 and 8 are not included.

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    5      
x2 =    7      
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    6      
          
          
Then          
          
P(at most    4   ) =    0.2850565
P(at most    7   ) =    0.74397976
          
Thus,          
          
P(between x1 and x2) =    0.45892326   [ANSWER]

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