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? type the number in the box.
Answer
Explanation:
Step1: Recall mean formula
The mean $\mu$ of a discrete - probability distribution is $\mu=\sum_{x}x\cdot P(x)$.
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 $x = 4$, $P(4)=0$; when $x = 5$, $P(5)=0.2$.
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 $x = 4$: $4\times0=0$. For $x = 5$: $5\times0.2 = 1$.
Step4: Sum up the products
$\mu=0.3 + 0.8+0.3 + 0+1=2.4$.
Answer:
$2.4$