Question

According to a 2015 Census Bureau survey, 75,511 of the 822,959 residents of Baltimore County, Maryland, were enrolled in college. Consider a sample of 800 residents of Baltimore County, Maryland in 2015 selected at random. Which of the following is closest to the expected value of the number in the sample enrolled in college?

Answer 1

Answer:

73.4

Step-by-step explanation:

-Given that 75,511 out of 822,959  residents enrolled in the college, the probability of success  is calculated as:

$P_{enrollment}=\frac{Enrollment}{Total \ Residents}\\\\=\frac{75511}{822959}\\\\=0.09176\\\\p=0.09176$

#We know that this is a binomial distribution with p=0.09176 and n=800, Expected value is calculated as:

$E(X)=np, n=800, p=0.09176\\\\=0.09176\times 800\\\\=73.4$

Hence the expected value E(X)=73.4