calculate the expected value of spinning the spinner one time. round to the nearest hundredth if…

calculate the expected value of spinning the spinner one time. round to the nearest hundredth if necessary.\nsample problem\n8(\\frac{1}{3}) + 6(\\frac{1}{3}) + 4(\\frac{1}{3}) = \\frac{8}{3}+2 + \\frac{4}{3}=6\nthe expected value is 6.

calculate the expected value of spinning the spinner one time. round to the nearest hundredth if necessary.\nsample problem\n8(\\frac{1}{3}) + 6(\\frac{1}{3}) + 4(\\frac{1}{3}) = \\frac{8}{3}+2 + \\frac{4}{3}=6\nthe expected value is 6.

Answer

Explanation:

Step1: Determine probabilities

The spinner is divided into 8 equal - sized sections, so the probability of landing on each section is $\frac{1}{8}$.

Step2: Calculate expected value

The values on the spinner are 1, 2, 3, 4, 4, 5, 5, 6. The expected value $E(X)$ is calculated as follows: [ \begin{align*} E(X)&=1\times\frac{1}{8}+2\times\frac{1}{8}+3\times\frac{1}{8}+4\times\frac{2}{8}+5\times\frac{2}{8}+6\times\frac{1}{8}\ &=\frac{1 + 2+3 + 8+10 + 6}{8}\ &=\frac{30}{8}\ & = 3.75 \end{align*} ]

Answer:

3.75