An important part of the customer service responsibilities of a natural gas util

Question

An important part of the customer service responsibilities of a natural gas utility company concerns the speed with which calls relating to no heat in a house can be serviced. Suppose that one service variable of importance refers to whether or not the repair person reaches the home within a two-hour period. Past data indicate that the likelihood is 0.75 that the repair person reaches the home within a two hour period.

a.) If a sample of eight service calls for “no heat” is selected, what is the probability that the repair person will arrive at five or more homes within the two-hour period?

b.) The natural gas utility company makes a claim in a TV advertisement: “We understand that waiting for a service call can be stressful for our customers. Therefore, we wish to back up our claim that 75% of our repair professionals reach a customer’s home within a two hour period. Should they fail to reach your home within the specified time-period, we will compensate you by subtracting $8 from your next gas bill.” What is the expected value of that commitment per service call?

Explanation / Answer

Here we will use binomial distribution with n=8 and p=0.75

P(X=x)=ncx*px*(1-P)n-x

1. P(X>=5)=0.8862 using binomial calculator

2.To find expected value we will calculate mean =n*P=8*0.75=6

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