The number of messages that arrive at a Web site is a Poisso

The number of messages that arrive at a Web site is a Poisson distributed random variable with a mean of 7 messages per hour. Round your answers to four What is the probability that 5 messages are received in 1 hour? What is the probability that 10 messages are received in 1.5 hours? What is the probability that less than 2 messages are received in 1/2 hour? Samples of rejuvenated mitochondria are mutated (defective) in 2% of cases. Suppose 12 samples are studied, and they can be considered to be independe No samples are mutated. At most one sample is mutated. More than half the samples are mutated. Round your answers to two decimal places (e.g. 98.76). The probability is .7847 The probability is I The probability is .9769 The probability is 0 The number of errors in a textbook follow a Poisson distribution with a mean of 0.02 errors per page. What is the probability that there are 3 or less errors in Round your answer to four decimal places (e.g. 98.7654).

Solution

THE NUMBER OF MESAGES THAT ARRIVE...

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 =    7      
          
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.127716668 [answer]

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b)

In 1.5 hours, the mean is 7*1.5 = 10.5.

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 =    10.5      
          
x = the number of successes =    10      
          
Thus, the probability is          
          
P (    10   ) =    0.123605529 [answer]

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c)

In 1/2 hour, the mean is 7*(1/2) = 3.5.

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 =    3.5      
p = the probability of a success =    0      
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   ) =    0.135888225
          
Which is also          
          
P(fewer than   2   ) =    0.135888225 [answer]

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