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For a large, top-rated corporation, 97% of employees said the corporation is a great place to work. Suppose that we will take a random sample of 7 employees. Let p represent the proportion of employees from the sample who said the corporation is a great place to work. Consider the sampling distribution of the sample proportion p.Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed.(a)Find μp (the mean of the sampling distribution of the sample proportion).=μp (b)Find σp (the standard deviation of the sampling distribution of the sample proportion).=σp

Question

For a large, top-rated corporation, 97% of employees said the corporation is a great place to work. Suppose that we will take a random sample of 7 employees. Let p represent the proportion of employees from the sample who said the corporation is a great place to work. Consider the sampling distribution of the sample proportion p.Complete the following. Carry your intermediate computations to four or more decimal places. Write your answers with two decimal places, rounding if needed.(a)Find μp (the mean of the sampling distribution of the sample proportion).=μp (b)Find σp (the standard deviation of the sampling distribution of the sample proportion).=σp

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Solution

(a) The mean of the sampling distribution of the sample proportion (μp) is equal to the population proportion (P). In this case, P is 0.97 (or 97%), so μp = 0.97.

(b) The standard deviation of the sampling distribution of the sample proportion (σp) can be found using the formula:

σp = sqrt[ P(1 - P) / n ]

where P is the population proportion and n is the sample size. Substituting the given values:

σp = sqrt[ 0.97(1 - 0.97) / 7 ] σp = sqrt[ 0.0291 / 7 ] σp = sqrt[ 0.0041571 ] σp = 0.0645 (rounded to four decimal places)

So, μp = 0.97 and σp = 0.06 (rounded to two decimal places).

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