Question

the table below shows the probability distribution of a random variable z.
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 \(\mu=\sum_{i}z_i\times P(z_i)\)

Step2: Calculate each term

For \(z = 14\) and \(P(14)=0.2\), the term is \(14\times0.2 = 2.8\)
For \(z = 15\) and \(P(15)=0.1\), the term is \(15\times0.1=1.5\)
For \(z = 16\) and \(P(16)=0.7\), the term is \(16\times0.7 = 11.2\)

Step3: Sum up the terms

\(\mu=2.8 + 1.5+11.2\)
\(\mu = 15.5\)

Answer:

\(15.5\)