Chapter 11, Problem 14SGR

To determine

To find: The expected number of dance recitals per year.

Answer to Problem 14SGR

The expected number of dance recitals per year is $1.51$ .

Explanation of Solution

Given:

The given table is as follows.

Number of dance Recitals per year
Recitals	0	$1$	$2$	$3$	$4$
Probability	$0.3$	$0.3$	$0.13$	$0.13$	$0.14$

Calculation:

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

The expected number of dance recitals per year can be calculated as follows.

  $\begin{array}{c}E\left(X\right)=0\left(0.3\right)+1\left(0.3\right)+2\left(0.13\right)+3\left(0.13\right)+4\left(0.14\right)\\ =1.51\end{array}$

Therefore, the expected number of dance recitals per year is $1.51$ .