A recent article in the Cincinnati Enquirer reported that the mean labor cost to

Question

A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Montes Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute Z values for each and comment on findings.

Explanation / Answer

? = 90 ? = 22 standardize x to z = (x - ?) / ? P(x > 75) = P( z > (75-90) / 22) = P(z > -0.6818) = 0.7517 (From Normal probability table) ? = 90 ? = 22 standardize x to z = (x - ?) / ? P(x > 100) = P( z > (100-90) / 22) = P(z > 0.4545) = 0.3264 (From Normal probability table) If the trend continued, it would have the following effect: For repeated repairs of the two pumps: Approximately 75% of pump 1 had cost greater than $75 Approximately 33% of pump 2 had cost greater than $100

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