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 \\( \square \\)
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the standard deviation

The formula for the standard deviation $\sigma$ is $\sigma=\sqrt{\sigma^{2}}$. Given that $\sigma^{2}=\mu = 2.7$.
$$\sigma=\sqrt{2.7}$$

Step2: Simplify the expression

Using a calculator, $\sqrt{2.7}\approx1.64$ (rounded to two decimal places).

Answer:

The standard deviation is approximately $1.64$.