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saveliy_v [14]
2 years ago
13

Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What

is the probability that the call center will get between 4,800 and 5,000 calls in a day
Mathematics
1 answer:
lakkis [162]2 years ago
4 0

Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 5,500 and standard deviation 1,000.

This means that \mu = 5500, \sigma = 1000

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

Z = \frac{X - \mu}{\sigma}

Z = \frac{5000 - 5500}{1000}

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

X = 4800

Z = \frac{X - \mu}{\sigma}

Z = \frac{4800 - 5500}{1000}

Z = -0.7

Z = -0.7 has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

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