A plumber works in a rural area with many customers over 100 miles from the shop

Question

A plumber works in a rural area with many customers over 100 miles from the shop. Based on prior experience, he knows that 7% of customers need a particular part which takes up quite a bit of room in his truck. He plans to see 11 customers in a day and wants at least a 90% chance of having enough of the part. How many should he carry on his truck?

Clearly state which probability distribution’s PMF you are using to perform this calculation as well as which value is to be given to each variable in the PMF. Then compute the answer to the question.

Explanation / Answer

This is a binomial distribution, where we need to find the maximum number of successes, x, to have AT LEAST A 90% probability that at most x successes out of n = 11 trials. Here, the probability of a success being 0.07.

Hence, we need to find so that P(at most x) >= 0.90.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.07      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.963020709

Hence, the least amount he should carry is 2 PARTS. [ANSWER: 2]

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