Question

use the probability distribution or histogram to find the (a) mean, (b)
variance, (c) standard deviation, and (d) expected value of the
probability distribution, and (e) interpret the results. the histogram
shows the distribution of household sizes in country a for a recent
year.
(c) the standard deviation is 1.45
(round to two decimal places as needed.)
(d) the expected value is 2.579
(type an integer or a decimal. do not round.)
(e) interpret your results. select all that apply.
a. most of the household sizes differ from the expected value by 2 or 3 people.
b. the average household is expected to have either 2 or 3 people.
c. most of the household sizes differ from the expected value by 1 or 2 people.
d. the average household is expected to have either 1 or 2 people.

Explanation:

• The expected value (mean) of \(2.579\) is close to \(2\) and \(3\). So, the average household is expected to have either \(2\) or \(3\) people (Option B).
• The standard deviation of \(1.45\) means that most data points (household sizes) are within \(1 - 2\) standard - deviation ranges from the mean. So, most of the household sizes differ from the expected value by \(1\) or \(2\) people (Option C).

Answer:

B. The average household is expected to have either 2 or 3 people.
C. Most of the household sizes differ from the expected value by 1 or 2 people.