HELP PLEASE!! QUANTITATIVE QUESTION PLEASE POST NUMERICAL RESPONSE 1. An applian

Question

HELP PLEASE!!

QUANTITATIVE QUESTION

PLEASE POST NUMERICAL RESPONSE

1. An appliance manufacturer wants to contract with a repair shop to hand authorized repairs in Indianapolis. The company set an acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 74 minutes with a standard deviation of 4.0 minutes. The other firm had a mean repair time of 72 minutes with a standard deviation of 5.1 minutes. Which firm would you choose? Why?

Explanation / Answer

The best choice is the firm with 74 minutes and the smaller standard deviation of 4 minutes.

The key to this question is that you want to choose the firm that will fall within the 50 - 90 minute range on the most reliable basis.

Looking at the mean times of 72 and 74 minutes for both choices, respectively, we see that they are close to exceeding the upper bound of 90 minutes than the lower bound of 50 minutes. So the 90 minute limit is what we have to be concerned about.

For the first firm with 74 minutes and a standard deviation of 4, to fall outside of the 90 minute time frame, the data would have to be:

(90 - 74) / 4 = 16/4 = 4 standard deviations outside of the mean

For the firm with 72 minutes and a standard deviation of 5.1, to fall outside of the 90 minute time frame, the data would have to be:

(90 - 72) / 5.1 = 18 / 5.1 = 3.53 standard deviations outside of the mean

Since the first choice requires 4 standard deviations outside of the mean, it is more likely to adhere to the time constraing boundaries than the second choice that only requires 3.53 standard deviations from the mean to fall outside of the constraints.

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