This table shows the relationship between the number of workers assigned to a project and the number of days it will take them t
o complete the project.
Workers Days
2 42
3 28
6 14
12 7
Use the relationship in the table to complete the statements.
Select the correct answer from each drop-down menu.
As the number of workers increases, the number of days it will take to complete the project ________. The ______ of the two variables is constant.
The number of days it takes for a construction project to be completed varies ____ as the number of workers assigned to the project.
Workers Days
2 42
3 28
6 14
12 7
Use the relationship in the table to complete the statements.
Select the correct answer from each drop-down menu.
As the number of workers increases, the number of days it will take to complete the project ________. The ______ of the two variables is constant.
The number of days it takes for a construction project to be completed varies ____ as the number of workers assigned to the project.
1 answer:
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Answer:
Explained below.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
(a)
The sample selected is of size <em>n</em> = 450 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
So, the sampling distribution of sample proportion is .
(b)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.
(c)
The sample selected is of size <em>n</em> = 200 > 30.
Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.
The mean and standard deviation are:
So, the sampling distribution of sample proportion is .
(d)
Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:
Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.
(e)
The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.
And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.
So, there is a gain in precision on increasing the sample size.