Question

the table below shows the probability distribution of a random variable x.
what is the mean of the probability distribution?
write your answer as a decimal.

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The mean formula is $\mu=\sum xP(x)$.

Step2: Calculate each term

For $x = 15$ and $P(x)=0.6$: $15\times0.6 = 9$.
For $x = 16$ and $P(x)=0.1$: $16\times0.1=1.6$.
For $x = 17$ and $P(x)=0.3$: $17\times0.3 = 5.1$.

Step3: Sum up the terms

$\mu=9 + 1.6+5.1$.

Answer:

$15.7$