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 for discrete - random variable

The mean $\mu$ of a discrete - random variable $X$ with probability distribution $P(X)$ is given by $\mu=\sum_{x}x\cdot P(x)$. From the graph, when $x = 1$, $P(1)=0.3$; when $x = 2$, $P(2)=0.4$; when $x = 3$, $P(3)=0.2$; when $x = 5$, $P(5)=0.3$ (assuming the height of the bar at $x = 5$ is $0.3$ as it seems to be at the same height as the bar at $x = 1$).

Step2: Calculate the product for each $x$ 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 $x = 3$: $3\times P(3)=3\times0.2 = 0.6$.
For $x = 5$: $5\times P(5)=5\times0.3 = 1.5$.

Step3: Sum up the products

$\mu=0.3 + 0.8+0.6 + 1.5=3.2$.

Answer:

$3.2$