a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean…
a project is graded on a scale of 1 to 5. if the random variable, x, is the project grade, what is the mean of the probability distribution below? probability distribution 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 x 0.2 0.4 1 3
Answer
Explanation:
Step1: Identify probabilities
From the bar - chart, $P(X = 1)=0.1$, $P(X = 2)=0.2$, $P(X = 3)=0.4$, $P(X = 4)=0.2$, $P(X = 5)=0.1$.
Step2: Recall mean formula
The mean $\mu$ of a discrete probability distribution is $\mu=\sum_{i}x_{i}P(X = x_{i})$.
Step3: Calculate the mean
$\mu=(1\times0.1)+(2\times0.2)+(3\times0.4)+(4\times0.2)+(5\times0.1)$ $=0.1 + 0.4+1.2 + 0.8+0.5$ $=3$
Answer:
3