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Answer :
The question is related to the sampling distribution concept. For an infinite population with proportion 0.4, when taking a random sample of size 96, the mean (μ) of sample distribution is 0.4 (population proportion) and the standard deviation (σ) is 0.05, calculated using the formula √[(P(1-P))/n] where P = 0.4 and n = 96.
This question is related to statistics, and more specifically, the concept of sampling distribution. When we take a random sample of size n from a population, the proportion in that sample is a random variable that follows a normal distribution if certain conditions are met. The conditions are usually that n (sample size) is large, the population is infinite, and the samples are independent.
In this case, the population proportion is given as 0.4 which is the mean of the sample distribution (μ). The standard deviation (σ) of the sample distribution is calculated using the formula √[(P(1-P))/n], where P is the population proportion and n is the sample size. By substituting P = 0.4 and n = 96 into the formula, we get σ = √[(0.4 * 0.6) / 96] = 0.05.
So, the correct answer to this question is (c) 0.4 and 0.05.
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