Question

the mean number of bankruptcies filed per hour by businesses in a country one year was about 2.7.
(a) find the variance and standard deviation using the fact that the variance of a poisson distribution is ( sigma^{2}=mu ). interpret the results.
(b) identify the least number of bankruptcies during an hour that you would consider unusual.
click the icon to view the table of poisson probabilities.
(a) the variance is 2.7
(type an integer or a decimal. do not round)
the standard deviation is 1.64
(round to two decimal places as needed.)
interpret the results choose the correct answer below.
a. the number of bankruptcies is always the standard deviation number of bankruptcies
b. the number of bankruptcies usually differs from the mean by no more than the standard deviation number of bankruptcies
c. the number of bankruptcies differs from the standard deviation by no more than the mean number of bankruptcies
d. the number of bankruptcies always differs from the mean by no more than the standard deviation number of bankruptcies
(b) at least businesses filing in any given hour would be unusual
(type a whole number)

Explanation:

Step1: Calculate standard deviation

Given variance \(\sigma^{2}=\mu = 2.7\). Standard deviation \(\sigma=\sqrt{\mu}\). So \(\sigma=\sqrt{2.7}\approx1.64\)

Step2: Use empirical rule (for non - normal, we can still use the idea that values more than \(2\sigma\) from the mean are unusual)

The mean \(\mu = 2.7\), \(\mu+2\sigma=2.7 + 2\times1.64=2.7+3.28 = 5.98\approx6\)

Answer:

(a) The variance is \(2.7\), the standard deviation is \(1.64\). The correct interpretation is B. (b) At least \(6\)