expected value pre - test active 1 2 3 4 5 6 time remaining 57:05 the marketing club at school is opening a…

Explanation:

Step1: Recall expected - value formula

The formula for the expected value $E(X)=\sum_{i = 1}^{n}x_ip_i$, where $x_i$ is the value of the random - variable and $p_i$ is the probability of that value. Here, the number of students is $n = 50$, and $p_i=\frac{\text{Number of students}}{\text{Total number of students}}$, $x_i$ is the dollars spent on lunch each day.

Step2: Calculate the products

For $x_1 = 10$ and number of students $n_1 = 2$, $p_1=\frac{2}{50}$, and $x_1p_1=10\times\frac{2}{50}=0.4$. For $x_2 = 8$ and number of students $n_2 = 1$, $p_2=\frac{1}{50}$, and $x_2p_2=8\times\frac{1}{50}=0.16$. For $x_3 = 6$ and number of students $n_3 = 12$, $p_3=\frac{12}{50}$, and $x_3p_3=6\times\frac{12}{50}=1.44$. For $x_4 = 5$ and number of students $n_4 = 23$, $p_4=\frac{23}{50}$, and $x_4p_4=5\times\frac{23}{50}=2.3$. For $x_5 = 4$ and number of students $n_5 = 8$, $p_5=\frac{8}{50}$, and $x_5p_5=4\times\frac{8}{50}=0.64$. For $x_6 = 3$ and number of students $n_6 = 4$, $p_6=\frac{4}{50}$, and $x_6p_6=3\times\frac{4}{50}=0.24$.

Step3: Sum up the products

$E(X)=0.4 + 0.16+1.44 + 2.3+0.64+0.24=5.2$.

Answer:

$5.2$