40 points [statistics] distributions of sample ranges, means, and medians.
1. samples of size n = 150 are randomly selected from the u. s. census data, and the income range is found for each sample. what is the distribution of the sample ranges?
skewed to the right
normal (approximately)
skewed to the left
not enough information provided
2. samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. what is the distribution of the sample means?
normal (approximately)
not enough information provided
skewed to the right
skewed to the left
3. samples of size n = 250 are randomly selected from the u. s. census data, and the median income is found for each sample. what is the distribution of the sample medians?
normal (approximately)
not enough information provided
skewed to the left
skewed to the right

The correct answer for this question is this one:

1. Samples of size n = 150 are randomly selected from the U.S. census data, and the income range is found for each sample. What is the distribution of the sample ranges?

skewed to the right
normal (approximately)
skewed to the left
not enough information provided

2. Samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. What is the distribution of the sample means?

normal (approximately)
not enough information provided
skewed to the right
skewed to the left

3. Samples of size n = 250 are randomly selected from the U.S. census data, and the median income is found for each sample. What is the distribution of the sample medians?

normal (approximately)
not enough information provided
skewed to the left
skewed to the right
Hope this helps answer your question and have a nice day ahead.

Hold on lemme do the work

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.