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What Is the Expected Value for the Binomial Distribution Below? 100 Households

What is the expected value for the binomial distribution below? Use n=100 households and p=0.65 to calculate and interpret E(X)=65 households.

Question

In a community, 65% of households have at least one college graduate. A random sample contains 100 households. Let X count the sampled households with at least one college graduate. Find the mean of X.

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Evidence boundary

This answers OpenStax Practice Test 2, question 22 with its shared household stem: n=100 and p=0.65. It is a complete text-based representative exercise, not a reconstruction of an unspecified graph. The binomial assumption is stated explicitly; 65 is an expectation, not an observed result.