Question

the random variable x is the crew size of a randomly selected shuttle mission. its probability distribution is shown below. complete parts a through c.

a. find and interpret the mean of the random variable.

μ = 5.624 (round to three decimal places as needed.)

interpret the mean. choose the correct answer below.

o a. the observed value of the random variable will be less than the mean of the random variable in most observations.

o b. as the number of observations, n, increases, the mean of the observations will approach the mean of the random variable.

o c. as the number of observations, n, decreases, the mean of the observations will approach the mean of the random variable.

o d. the observed value of the random variable will be equal to the mean of the random variable in most observations.

Explanation:

Step1: Calculate the mean

The formula for the mean of a discrete random variable is \(\mu=\sum xP(x)\).

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Step2: Interpret the mean

The mean of a discrete random variable represents the long - term average value of the variable. As the number of observations \(n\) increases, the mean of the observations will approach the mean of the random variable. This is in line with the Law of Large Numbers.

Answer:

\(\mu = 5.624\). The correct interpretation is B. As the number of observations, \(n\), increases, the mean of the observations will approach the mean of the random variable.