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

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?

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?

Answer

Explanation:

Step1: Recall mean formula for discrete - probability distribution

The formula for the mean $\mu$ of a discrete - probability distribution is $\mu=\sum_{x}x\cdot P(x)$.

Step2: Identify values of $x$ and $P(x)$ 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 $P(4) = 0$).

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

For $x = 1$: $1\times0.3=0.3$. For $x = 2$: $2\times0.4 = 0.8$. For $x = 3$: $3\times0.1=0.3$. For $x = 5$: $5\times0.2 = 1$.

Step4: Sum up the products

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

Answer:

$2.4$