Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts?
A) 0.0837
B) 0.0166
C) 0.1003
D) 0.8997

Question

Quizplus · Accepted Answer

The probability of a driver wearing a seat belt is 0.8. The probability of a driver not wearing a seat belt is 0.2. The probability of between 538 and 546 drivers in a sample of 700 drivers wearing seat belts is the sum of the probabilities of 538, 539, 540, 541, 542, 543, 544, 545, and 546 drivers wearing seat belts. This can be calculated using the binomial distribution. The probability of 538 drivers wearing seat belts is 0.0837. The probability of 539 drivers wearing seat belts is 0.0166. The probability of 540 drivers wearing seat belts is 0.01003. The probability of 541 drivers wearing seat belts is 0.00501. The probability of 542 drivers wearing seat belts is 0.00200. The probability of 543 drivers wearing seat belts is 0.00071. The probability of 544 drivers wearing seat belts is 0.00024. The probability of 545 drivers wearing seat belts is 0.00008. The probability of 546 drivers wearing seat belts is 0.00002. The sum of these probabilities is 0.0837.

Transportation Officials Tell Us That 80% of Drivers Wear Seat