Question

A store owner will change the stock of snowboards for the next year if the average demand over the 12 winter Saturdays in a season (considered a random sample) is over 154 or under 134. These limits aren’t equidistant from the long-run process mean of 147 because the costs of oversupply and undersupply are different. If the population mean stays at 147. What is the probability that the manager will change the stock?

Answer 1

Let X be the average demand on winter Saturdays                  
Average demand on winter Saturdays is 147                  
                  
Then, X follows a Poisson distribution with λ = 147                  
Manager will change stock if X is greater than 154 or less than 134                  
To find P(Manager will change stock)                  
that is to find P(X > 154 or X < 134)                  
P(X > 154 or X < 134)                  
     = 1 - P(134 ≤ X ≤ 154)                  
         = 1 - [P(X ≤ 154) - P(X ≤ 134)]                   
We use Excel function POISSON.DIST to find the probability                  
       = 1 - (POISSON.DIST(154, 147, TRUE) - POISSON.DIST(134, 147, TRUE))                  
       = 1 - (0.734697 - 0.150995)                  
       = 0.416298                  

P(Manager will change stock) = 0.4163                  

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