Question

consider the probability distribution shown for the random variable x found below. complete part a through f.
x 5 6 8 14
p(x) 0.4 0.2 0.2 0.2
...
c. find σ.
σ = 3.3823 (round to four decimal places as needed.)
d. interpret the value you obtained for μ. choose the correct answer below.
○ a. the average value of x over many trials will be less than μ.
○ b. the average value of x over many trials will be more than μ.
○ c. the average value of x over many trials is equal to μ

Explanation:

The expected value (μ) of a random variable represents the long - run average value of the random variable over many independent trials. So, when we take the average value of \( x \) over a large number of trials, this average should be equal to \( \mu \). Option A says the average will be less than \( \mu \), which is incorrect. Option B says the average will be more than \( \mu \), which is also incorrect. Option C correctly states that the average value of \( x \) over many trials is equal to \( \mu \).

Answer:

C. The average value of x over many trials is equal to μ