Consider a sampling distribution with p equals 0.15p=0.15 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. a. For a random sample of size n equals 5000n=5000. b. For a random sample of size n equals 1000n=1000. c. For a random sample of size n equals 500n=500.

Step-by-step explanation:

a. Given p=0.15.

-The mean of a sampling proportion  of n=5000 is calculated as:

-The standard deviation is calculated using the formula:

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050

b. Given that p=0.15 and n=1000

#The mean of a sampling proportion  of n=1000 is calculated as:

#-The standard deviation is calculated as follows:

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113

c. For p=0.15 and n=500

#The mean is calculated as follows:

#The standard deviation of the sample proportion is calculated as:

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160

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step-by-step explanation: