Question

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Public Two-Year Colleges From the data in CollegeScores2yr we know that about 66% of two-year colleges in the US are public institutions. Suppose that we select samples of n = 90 schools at a time from the population of all two-year colleges and find the proportion of public schools in each sample.
Consider the distribution of these sample proportions when n 90 and p = 0.66.
What is its form?

Answer 1

The distribution of the sample proportions in this case follows a binomial distribution. As the sample size is large enough, the distribution can be approximated by a normal distribution. So, the form of the distribution can be considered approximately normal.

Step-by-step explanation:

The distribution of the sample proportions in this case follows a binomial distribution. A binomial distribution is a probability distribution of a random variable with two possible outcomes, where each outcome has a fixed probability. In this case, the two possible outcomes are public schools and non-public schools, and the probability of selecting a public school is 0.66.

The distribution of the sample proportions can be approximated by a normal distribution when the sample size is large enough, which is the case with n = 90. So, the form of the distribution can be considered approximately normal.

This means that as you take more samples of size 90 from the population of all two-year colleges, and calculate the proportion of public schools in each sample, the distribution of those sample proportions will resemble a normal distribution.