Question

in the probability distribution to the right, the random variable x represents the number of marriages an individual aged 15 years or older has been involved in. compute and interpret the mean of the random variable x.
$$ mu _ { x } = 0.923 $$ marriages
(type an integer or a decimal. do not round.)
which of the following interpretations of the mean is correct?
a. if many randomly selected individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
b. if many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals.
c. if many randomly selected individuals aged 40 to 49 years were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
d. if any individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.

Explanation:

Step1: Calculate the mean of the random variable \(X\)

The formula for the mean of a discrete random variable is \(\mu_X=\sum_{x}x\cdot P(x)\).

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Step2: Interpret the mean

The mean of a discrete random variable represents the long - term average value. If many individuals aged 15 years or older were randomly selected, the sample mean number of marriages should be close to the mean of the random variable.

Answer:

A. If many individuals aged 15 years or older were randomly selected, the observed number of marriages will be equal to the mean number of marriages for most individuals.