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 is divided into 4 equal - parts, so the probability of landing on each part is $\frac{1}{4}$. The values are 5, 4, 4, 1.

Step2: Calculate expected - value formula

The expected - value formula is $E(X)=\sum_{i = 1}^{n}x_ip_i$. Here, $n = 4$, $x_1 = 5$, $x_2 = 4$, $x_3 = 4$, $x_4 = 1$, and $p_1=p_2=p_3=p_4=\frac{1}{4}$.
\[

$$\begin{align*} E(X)&=5\times\frac{1}{4}+4\times\frac{1}{4}+4\times\frac{1}{4}+1\times\frac{1}{4}\\ &=\frac{5 + 4+4 + 1}{4}\\ &=\frac{14}{4}\\ & = 3.5 \end{align*}$$

\]

Answer:

3.5