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belka
28 days ago
10

A credit card company receives numerous phone calls throughout the day from customers reporting fraud and billing disputes. Most

of these callers are put "on hold" until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 2.5 minutes and a standard deviation 0.5 minutes. If 1.5% of the callers are put on hold for longer than x minutes, what is the value of x? Use Excel, and round your answer to two decimal places.
Computers and Technology
1 answer:
ivann1987 [1K]28 days ago
8 0
Approximately 3.59 minutes. The solution is derived using the z-score formula in Excel: Z-SCORE = (DataPoint - AVERAGE(DataSet)) / STDEV(DataSet). In Excel, AVERAGE computes the data set's mean while STDEV.S finds the standard deviation for a sample population. On the other hand, STDEV.P calculates this metric for the entire population. The z-score equation translates to x - μ/σ where: x =?? μ = 2.5 minutes and σ = 0.5 minutes. The question seeks the value of x such that 1.5% of callers hold for more than x minutes. Consequently, this reads: 100 - 1.5% gives 98.5%, or 0.985. Using Excel, the z-score for the 98.5 percentile computes to roughly 2.1701. Using the equation: 2.1701 = x - 2.5/0.5, we derive: 2.1701 × 0.5 = x - 2.5, leading to 1.08505 = x - 2.5 and therefore: x = 1.08505 + 2.5 = 3.58505. Rounded to two decimal places, this gives 3.59 minutes. Hence, 1.5% of the callers experienced hold times exceeding 3.59 minutes.
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