Match each key characteristic of a distribution with the concept it characterizes. 1. characterizes the spread of a group 2. characterizes the average value of a group 3. characterizes the average value of a subgroup 4. characterizes the distribution of a subgroup 5. characterizes percentages of a normal distribution a. sample meanb. z-valuesc. population meand. population standard deviatione. sample standard deviation

1 - D

2 - C

3 - A

4 - E

5 - B

Step-by-step explanation:

We have to match each key characteristic of a distribution with the concept it characterizes.

1. Characterizes the spread of a group

Here group refers to the population, thus the spread of population is given by population standard deviation

D. Population standard deviation

2. Characterizes the average value of a group

Here group refers to the population, thus, the average value of population is given by population mean.

C. Population mean

3. Characterizes the average value of a subgroup

Here the subgroup refers to the sample. The average value of sample is given by sample mean.

A. Sample mean

4. Characterizes the distribution of a subgroup

The subgroup refers to sample. It is characterized by sample standard deviation.

E. Sample standard deviation

5. Characterizes percentages of a normal distribution

z-values are used to characterize the percentages in a normal distribution.

B. Z-values

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option

what i would say the best answer is a. 40.5