Suppose 40% of all college students have a computer at home and a sample of 100 is taken.What is the probability that more than 50 of those in the sample have a computer at home?
A) 0.4793
B) 0.9793
C) 0.0207
D) 0.5207
E) 0.6754

Question

Quizplus · Accepted Answer

This problem requires the use of the binomial distribution since we are interested in the number of successes (students with a computer) out of a fixed sample size (n=100). Let X be the random variable representing the number of students with a computer. Then X~Bin(100,0.4) since the probability of success (having a computer) is p=0.4. To find the probability that more than 50 students have a computer, we need to sum the probabilities for X=51, X=52, ..., X=100. Doing this by hand can be tedious, so we can use a calculator or software to find this probability. Using an online calculator or software, we find that P(X>50) = 0.0207. Therefore, the best choice is (C).

Suppose 40% of All College Students Have a Computer at Home