A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let pd represent the population proportion of all cell phone screens with a screen defect, therefore pd=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, μpˆd=0.05. Which of the following is the best interpretation of μpˆd=0.05 ?

For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.

For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.
A

For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.

For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.
B

For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.

For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.
C

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
D

For all samples of size 400 from this population, the standard deviation of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

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Answer:

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

Step-by-step explanation:

College Board

Using the Central Limit Theorem, it is found that the correct option is:

C  For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

By the Central Limit Theorem, for a proportion p in a sample of size n, the mean of the sampling distribution of sample proportions is [tex]\mu = p[/tex], while the standard error is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex

In this problem, the mean of the sampling distribution of sample proportions is 0.05, that is, the mean proportion of all samples, hence, the correct option is C.

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