Question

use the fact that the variance of a poisson distribution is \\(\sigma^2 = \mu\\).
the mean number of bankruptcies filed per hour by businesses in a country was about seven. (a) find the variance and the standard deviation. interpret the results. (b) find the probability that at most five businesses will file bankruptcy in any given hour.

(a) the variance is 7.000.
(round to three decimal places as needed.)
the standard deviation is \\(\square\\)
(round to one decimal place as needed.)

Explanation:

Step1: Recall standard deviation formula

For a distribution, standard deviation \(\sigma\) is the square root of variance \(\sigma^2\). So \(\sigma=\sqrt{\sigma^2}\).

Step2: Substitute variance value

Given variance \(\sigma^2 = 7.000\), then \(\sigma=\sqrt{7}\). Calculate \(\sqrt{7}\approx2.64575\).

Step3: Round to one decimal place

Rounding \(2.64575\) to one decimal place, we look at the second decimal digit (4). Since \(4<5\), we keep the first decimal digit as is. So \(\sigma\approx2.6\).

Answer:

2.6