On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20 ? A) For all samples of size 20, the mean of all possible sample proportions is equal to 0.11.
B) For a randomly selected worker, the probability the worker will be more than 5 minutes late to work is 0.11.
C) For a random sample of 20 workers, the proportion of workers who are more than 20 minutes late to work will be 0.11.
D) For a random sample of 20 workers, the probability that 2.2 workers will be more than 5 minutes late to work is very high.
E) For repeated samples of size 20, the proportion of workers who are more than 5 minutes late to work varies in each sample by no more than 0.11.

The interpretation of the mean of the sampling distribution will be A. For all samples of size 20, the mean of all possible sample proportions is equal to 0.11.

In conclusion, the best option is A.

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A) For all samples of size 20, the mean of all possible sample proportions is equal to 0.11.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

In this question, we have that:

The proportion workers at a factory who are more than 5 minutes late to work is 0.11. So, by the interpretation of the central limit theorem, the mean of all sample proportions, for samples of size 20, will be of 0.11.

The correct answer is given by option A.

step-by-step explanation:

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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.