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. complete parts (a) through (f)

marriages for most individuals.

if many individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable

if any number of individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable

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

(d) compute the standard deviation of the random variable x

σx = □ marriages

(round to one decimal place as needed)

Explanation:

Step1: Calculate the mean ($\mu$)

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

$$
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$$

Step2: Calculate $\sum(x - \mu)^2\cdot P(x)$

$$
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$$

Step3: Calculate the standard deviation ($\sigma$)

The formula for the standard deviation of a discrete random variable is $\sigma=\sqrt{\sum(x - \mu)^2\cdot P(x)}$.

$$ \sigma=\sqrt{0.7221621}\approx0.9 $$

Answer:

$0.9$