Let the random variable X represent the number of people living in a household in a certain town. The standard deviation of X is 1.8. Which of the following statements is the best interpretation of the standard deviation?

A) The number of people living in a randomly selected household is expected to be 1.8 people.
B) The number of people living in a randomly selected household will be 1.8 people away from the mean
C) On average, the number of people living in a household varies from the mean by about 1.8 people.
D) For a random sample of households, the average number of people per household is expected to be 1.8 people
E) For a random sample of households, the average number of people per household will be 18 people away from the mean.

C) On average, the number of people living in a household varies from the mean by about 1.8 people

Step-by-step explanation:

Standard Deviation is a statistical measure of magnitude of variation/ dispersion, of a set of values from the mean of the set.

Low standard deviation implies values are closer to the mean. High standard deviation implies values are far/ wide spread around the mean.

If X represents number of people living in a household in a certain town ; standard deviation reflects average level of variation around the mean people living in a household's town.

So, standard deviation = 1.8 implies : On average, the number of people living in a household varies from the mean by about 1.8 people.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is