Need help with part B Show all steps You may need to use the appropriate table i

Question

Need help with part B Show all steps You may need to use the appropriate table in the Appendix of Tables to answer this question An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.5 year. How many loads can be expected to occur during a 4-year period? What is the probability that more than ten loads occur a 4-year period? (Round your answer to three decimal places.) How long must a time period be so that the probability of no loads occurring during that period is at most 0.1? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

b)

As there are 0.5 a year, then in 4 years there are 0.5*4 = 2 occurrences on average.

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 =    2      
          
x = our critical value of successes =    10      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   10   ) =    0.999991692
          
Thus, the probability of at least   11   successes is  
          
P(more than   10   ) =    8.30822*10^-6 [ANSWER]]

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