In one city,police estimate that 79% of drivers wear their seat belts.They set up a safety roadblock and they stop drivers to check for seat belt use.If 150 drivers are stopped,is it appropriate to use a Normal model to approximate the distribution of the number whose seat belt is not buckled?

Question

Quizplus · Accepted Answer

We can use the Normal approximation to approximate the distribution of the number of drivers whose seat belt is not buckled, as long as both np and nq are greater than or equal to 10.

Here, p = 1 - 0.79 = 0.21 is the probability that a driver's seat belt is not buckled, and n = 150 is the sample size.

So, np = 150 * 0.21 = 31.5 and nq = 150 * 0.79 = 118.5 are both greater than 10.

Thus, we can use the Normal model with μ = np = 31.5 and σ = sqrt(npq) = 4.99 to approximate the distribution of the number of drivers whose seat belt is not buckled. Therefore, the answer is D.

In One City,police Estimate That 79% of Drivers Wear Their