Question

calculate the expected value of spinning the spinner one time. round to the nearest hundredth if necessary. sample problem 8(1/3)+6(1/3)+4(1/3)=8/3 + 2+4/3 = 6 the expected value is 6. > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Identify probabilities and values

The spinner has 8 equal - sized sections. The probability of landing on each number is $\frac{1}{8}$. The values on the spinner are 1, 2, 3, 4, 5, 6, 7, 8.

Step2: Calculate the expected - value formula

The expected - value formula is $E(X)=\sum_{i = 1}^{n}x_ip_i$. Here, $x_i$ are the values on the spinner and $p_i=\frac{1}{8}$ for all $i$.
\[

$$\begin{align*} E(X)&=1\times\frac{1}{8}+2\times\frac{1}{8}+3\times\frac{1}{8}+4\times\frac{1}{8}+5\times\frac{1}{8}+6\times\frac{1}{8}+7\times\frac{1}{8}+8\times\frac{1}{8}\\ &=\frac{1 + 2+3+4+5+6+7+8}{8}\\ &=\frac{\frac{8\times(8 + 1)}{2}}{8}\\ &=\frac{36}{8}\\ & = 4.5 \end{align*}$$

\]

Answer:

4.5