Suppose 40% of all seniors 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

The sample size (100) is large enough for us to use the normal approximation to the binomial distribution. The mean of the binomial distribution is np = 100*0.4 = 40, and the standard deviation is sqrt(np(1-p)) = sqrt(100*0.4*0.6) = 4.899. We can use the following formula to standardize the random variable:

z = (x - np) / sqrt(np(1-p))

where x is the number of seniors in the sample who have a computer at home. We want to find the probability that more than 50 seniors in the sample have a computer at home, which is equivalent to finding the probability that z is greater than (50 - 40) / 4.899 = 2.04. Using a standard normal table or calculator, we find the probability to be approximately 0.0207. Therefore, the correct choice is C.

Suppose 40% of All Seniors Have a Computer at Home