Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 656 and 665 drivers in a sample of 850 drivers wear seat belts?
A)0.8925
B)0.0896
C)0.0179
D)0.1075

Question

Quizplus · Accepted Answer

This is a binomial probability problem, but given the large sample size, we can approximate it using a normal distribution. The mean number of drivers wearing seat belts is 850 * 0.8 = 680, and the standard deviation is sqrt(850 * 0.8 * 0.2) ≈ 13.416. Converting the range 656 to 665 into z-scores and looking up these values in a standard normal distribution table or using a calculator, we find the probability of being between these values is approximately 0.0896.

Transportation Officials Tell Us That 80% of Drivers Wear Seat