members of a step team perform dances involving stepping and clapping in unison. the random variable (x)…

Explanation:

Step1: Recall mean formula

The mean $\mu$ of a discrete - probability distribution is given by $\mu=\sum_{x}x\cdot P(x)$. We need to find the product of each value of $x$ and its corresponding probability $P(x)$ and sum them up.

Step2: Identify values from the graph

From the graph, when $x = 1$, $P(1)=0.3$; when $x = 2$, $P(2)=0.4$; when $x = 3$, $P(3)=0.1$; when $x = 5$, $P(5)=0.2$ (since there is no bar at $x = 4$, $P(4)=0$).

Step3: Calculate $x\cdot P(x)$ for each $x$

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 $x = 5$: $5\times P(5)=5\times0.2 = 1$.

Step4: Sum up the products

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

Answer:

$2.4$