the table below shows the probability distribution of a random variable z.\nwhat is the expected value of…

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value ( E(Z)) of a discrete random variable is ( E(Z)=\sum_{i}z_{i}P(z_{i})), where ( z_{i}) are the values of the random variable and ( P(z_{i})) are their corresponding probabilities.

Step2: Substitute the values into the formula

For ( z = 7) and ( P(7)=0.2), the contribution is ( 7\times0.2). For ( z = 8) and ( P(8)=0.6), the contribution is ( 8\times0.6). For ( z = 9) and ( P(9)=0.2), the contribution is ( 9\times0.2). So, ( E(Z)=(7\times0.2)+(8\times0.6)+(9\times0.2))

Step3: Calculate each term

( 7\times0.2 = 1.4), ( 8\times0.6=4.8), ( 9\times0.2 = 1.8)

Step4: Sum the terms

( E(Z)=1.4 + 4.8+1.8) ( E(Z)=8.0)

Answer:

(8.0)