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: Determine probabilities

Since the spinner is divided into 4 equal - sized sections, the probability of landing on each section is $\frac{1}{4}$.

Step2: Calculate expected - value formula

The expected value $E(X)$ is given by $E(X)=\sum_{i = 1}^{n}x_ip_i$, where $x_i$ are the possible outcomes and $p_i$ are their probabilities. Here, $x_1 = 6$, $x_2=9$, $x_3 = 12$, $x_4 = 25$ and $p_1=p_2=p_3=p_4=\frac{1}{4}$.
So, $E(X)=6\times\frac{1}{4}+9\times\frac{1}{4}+12\times\frac{1}{4}+25\times\frac{1}{4}$.

Step3: Simplify the expression

$E(X)=\frac{6 + 9+12 + 25}{4}=\frac{52}{4}=13$.

Answer:

13