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 number is $\frac{1}{4}$. The values are 5, 8, 9, and 12.

Step2: Calculate expected - value formula

The expected - value formula is $E(X)=\sum_{i = 1}^{n}x_ip_i$. Here, $x_1 = 5$, $p_1=\frac{1}{4}$, $x_2 = 8$, $p_2=\frac{1}{4}$, $x_3 = 9$, $p_3=\frac{1}{4}$, $x_4 = 12$, $p_4=\frac{1}{4}$.
$E(X)=5\times\frac{1}{4}+8\times\frac{1}{4}+9\times\frac{1}{4}+12\times\frac{1}{4}$

Step3: Simplify the expression

$E(X)=\frac{5 + 8+9 + 12}{4}=\frac{34}{4}=8.5$

Answer:

8.5