Question

A business has five customer service telephone lines. Let x denote the number of lines in use at any given time. Suppose that the probability distribution of x is as follows:

Find the standard deviation of x. Round your answer to two decimal places.

Answer 1

To calculate the standard deviation of x, the number of telephone lines in use, we would typically use a formula involving the mean and probabilities of each value of x. However, without the complete probability distribution provided, we cannot compute the standard deviation.

Step-by-step explanation:

The probability distribution of x, the number of telephone lines in use at any given time, is not fully provided in the question. To calculate the standard deviation of x, we would typically use the formula:

\[\sigma = \sqrt{\sum{(x_i - \mu)^2 \cdot P(x_i)}}\]

where \(x_i\) are the values of x, \(\mu\) is the mean of the distribution, and \(P(x_i)\) is the probability of \(x_i\). Without the complete probability distribution, we cannot compute the standard deviation. Nevertheless, if we had a Poisson or an Exponential distribution with known parameters, like the ones provided in reference texts, the standard deviation would be equal to the square root of the mean for a Poisson distribution and equal to the reciprocal of the rate parameter for an Exponential distribution.

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