Question

members of a step team perform dances involving stepping and clapping in unison. the random variable x represents the number of years of stepping experience that each member of the team has. the probability distribution, p(x), for the random variable x is shown on the graph below. what is the mean of the probability distribution? type the number in the box.

Explanation:

Step1: Recall mean formula

The mean $\mu$ of a discrete - probability distribution is given by $\mu=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the values of the random variable and $P(x_{i})$ are their corresponding probabilities.
From the graph: $P(1) = 0.3$, $P(2)=0.4$, $P(3)=0.1$, $P(5)=0.2$, and $P(4) = 0$.

Step2: Calculate the product for each value

For $x = 1$: $1\times P(1)=1\times0.3 = 0.3$
For $x = 2$: $2\times P(2)=2\times0.4 = 0.8$
For $x = 3$: $3\times P(3)=3\times0.1 = 0.3$
For $x = 4$: $4\times P(4)=4\times0 = 0$
For $x = 5$: $5\times P(5)=5\times0.2 = 1$

Step3: Sum up the products

$\mu=0.3 + 0.8+0.3 + 0+1$
$\mu=2.4$

Answer:

$2.4$