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Random samples of size 100 taken from a population with a proportion of 0.8, what are the mean and standard deviation of the distribution of sample proportions?

A. Mean = 0.8, Standard deviation = 0.08
B. Mean = 0.8, Standard deviation = 0.04
C. Mean = 0.5, Standard deviation = 0.05
D. Mean = 0.5, Standard deviation = 0.04

User Nemoo
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Final answer:

The mean of the distribution of sample proportions is 0.8, and the standard deviation is calculated using the square root of the product of population proportion, its complement, and the inverse of sample size (0.04), making the correct answer B.

The correct option is B.

Step-by-step explanation:

When dealing with random samples of size 100 taken from a population with a proportion of 0.8, the mean (μ) of the distribution of sample proportions is equal to the population proportion, which is 0.8. The standard deviation (σ) of the distribution of sample proportions can be calculated using the formula for the standard deviation of a proportion, which is σ = √(p(1-p)/n), where 'p' is the population proportion and 'n' is the sample size.

Using the given values, p = 0.8 and n = 100, we get:
σ = √(0.8(1-0.8)/100) = √(0.8(0.2)/100) = √(0.16/100) = √0.0016 = 0.04

Therefore, the correct answer for the mean and standard deviation of the distribution of sample proportions is B. Mean = 0.8, Standard deviation = 0.04.

The correct option is B.

User Abhishek Dutt
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