Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. Assume the variable follows a Poisson distribution. What is the probability that the company will receive more than 20 calls per hour? Round answer to 4 decimal places.

0.0409 = 4.09% probability that the company will receive more than 20 calls per hour

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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 pvalue, we get the probability that the value of the measure is greater than X.

The normal approximation can be used to a Poisson distribution, with

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance.

This means that .

Then

What is the probability that the company will receive more than 20 calls per hour?

Using continuity correction, this is , which is 1 subtracted by the pvalue of Z when X = 20.5. So

has a pvalue of 0.9591

1 - 0.9591 = 0.0409

0.0409 = 4.09% probability that the company will receive more than 20 calls per hour