Final answer:
The sampling distribution of the proportion, given p = 0.8 and n = 50, can be approximated using a normal distribution N(0.8, sqrt(0.8*0.2/50)). The necessary conditions for this approximation are satisfied, and the standard deviation is sqrt(8).
Step-by-step explanation:
Given that p = 0.8 and n = 50, we're looking to determine the sampling distribution of a proportion. In this problem, we are dealing with a large sample size, and because p is the probability of success in a single trial, the distribution of the sample proportion can be approximated using the normal distribution.
To utilize the normal distribution for proportions, we must check that the conditions np > 5 and nq > 5 are satisfied, where q is the probability of failure (q = 1 - p). In this case, np = 50(0.8) = 40 and nq = 50(1 - 0.8) = 50(0.2) = 10, so both conditions are met. Therefore, the sampling distribution of the sample proportion can be approximated as N(0.8, sqrt(0.8*0.2/50)).
To calculate the standard deviation of the sampling distribution, we use the formula σ = sqrt(npq). Substituting the values given, we get σ = sqrt(50*0.8*0.2), which simplifies to σ = sqrt(8). Consequently, this is the standard deviation of the sampling distribution of the sample proportion p'.