Suppose 40% of all college students have a computer at home and a sample of 64 is taken.Which is closest to 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

The probability that more than 30 students have a computer at home can be found using the normal approximation to the binomial distribution. The mean (μ) of the distribution is n*p = 64*0.40 = 25.6, and the standard deviation (σ) is sqrt(n*p*(1-p)) = sqrt(64*0.40*0.60) ≈ 3.92. To find the probability of more than 30 students, we calculate the z-score for 30.5 (for continuity correction) as (30.5-25.6)/3.92 ≈ 1.25. Looking up this z-score in a standard normal distribution table or using a calculator gives a right-tail probability of approximately 0.1314, indicating that the probability more than 30 students have a computer at home is closest to 0.1314.

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