Chapter 11, Problem 15SGR

To determine

To find: The expected number of snow days this year.

Answer to Problem 15SGR

The expected number of snow days this year is $1.88$ .

Explanation of Solution

Given:

The given table is as follows.

Number of Snow Days per year
Snow Days	0	$1$	$2$	$3$	4
Frequency	4	8	6	3	5

Calculation:

Calculate the expected value by using formula $E\left(X\right)={\displaystyle \sum \left[X\cdot P\left(X\right)\right]}$ .

The formula to calculate the probability is given by $P=\frac{\text{frequency}}{\text{Total}\text{number}\text{of}\text{snows}}$ .

The expected number of snow days this year can be calculated as follows.

  $\begin{array}{c}E\left(X\right)=0\left(\frac{4}{26}\right)+1\left(\frac{8}{26}\right)+2\left(\frac{6}{26}\right)+3\left(\frac{3}{26}\right)+4\left(\frac{5}{26}\right)\\ \approx 1.88\end{array}$

Therefore, the expected number of snow days this year is $1.88$ .