3. With infections running wild in many hospitals, the chief administrator of Lo

Question

3. With infections running wild in many hospitals, the chief administrator of Local Hospital decided to find out how Local Hospital stacks up against the national norm [national norm states that the average number of bacteria per square yard of surface area should be no more than 9 bacteria/square yard]. The number of bacteria per square yard is assumed to be a poisson random variable. Assume that your hospital is at the maximum of the norm [true average = 9 bacteria/square yard] a. If you go into the hospital, randomly sample one square yard of surface area, and count the number of bacteria found, calculate the probability of finding 19 or fewer bacteria.

Explanation / Answer

3.

a)

Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    9      
          
x = the maximum number of successes =    19      
          
Then the cumulative probability is          
          
P(at most   19   ) =    0.998944046 [ANSWER]

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