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.

x	2	3	4	5	6	7	8
p(x = x)	0.046	0.034	0.039	0.302	0.192	0.305	0.082

μ = 5.803 (round to three decimal places as needed.)
interpret the mean. choose the correct answer below.
a. as the number of observations, n, decreases, the mean of the observations will approach the mean of the random variable.
b. as the number of observations, n, increases, the mean of the observations will approach the mean of the random variable.
c. the observed value of the random variable will be equal to the mean of the random variable in most observations.
d. the observed value of the random variable will be less than the mean of the random variable in most observations.

Explanation:

The law of large numbers states that as the sample size (number of observations $n$) increases, the sample mean approaches the population mean (mean of the random - variable).

Answer:

B. As the number of observations, n, increases, the mean of the observations will approach the mean of the random variable.