Suppose 40% of all seniors have a computer at home and a sample of 64 is taken.What is the probability that more than 30 of those in the sample have a computer at home?
A)0.3686
B)0.1314
C)0.8686
D)0.6314
E)0.1343

Question

Quizplus · Accepted Answer

This is a binomial distribution problem with n=64, p=0.4 (probability of success), and we want to find P(X>30). We can use the normal approximation to the binomial distribution since n*p=64*0.4=25.6 and n*(1-p)=64*0.6=38.4 are both greater than 10. First, we standardize the distribution:
z = (30 - np) / sqrt(np(1-p))
= (30 - 25.6) / sqrt(64*0.4*0.6)
= 1.25
Then, we find the probability using the standard normal distribution table or calculator:
P(X > 30) = P(Z > 1.25)
= 0.1056
Therefore, the answer is B) 0.1314.

Suppose 40% of All Seniors Have a Computer at Home