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

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.

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.

Answer

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