Probability Simulation: Texting and Driving

Anything that takes your attention away from driving can be a distraction. Sending a text message, talking on the phone, using a GPS, and eating while driving are a few examples of distracted driving, all of which can endanger the driver and others. However, texting while driving is especially dangerous.When you send or read a text message, you take your eyes off the road for about 5 seconds which long enough to cover the lengtha football field while driving at 55 mph (Distracted Driving Activities, CDC).

Part I: Replicating Previous Studies

According to various studies (Braitman & McCartt, He et al, and Trivedi et al for example), drivers between the ages of 18 and 24 text and drive much more frequently than other drivers, with approximately 45% of participants saying they read and type texts while driving.

While the research is sound, it's a bit dated. The most recent publication was in 2017, so the data was most likely collected in 2016. Using the previous research as a guide, you decide to replicate the studies and poll 300 Iredell County residents with a driver's license between the ages of 18 and 24 (We won't worry about how you got your sample for this scenario...we'll just assume that it is sound and results in a fair, representative sample ). Assuming that the probability that a driver between the ages of 18 and 24 texts and drives is 45%, answer the following questions. For questions that require calculations, type what you put in the calculator and the answer.

1.First, confirm that this is a binomial distribution.

a.Is there a fixed number of trials? How many?

b.Are their two categories of outcomes? What are they?

c.Are the trials are independent? How do you know?

2.Identify the variables in this problem.

a.Number of trials (n):

b.Probability of success on any one trial (p):

c.Probability of failure on any one trial (q):

3.Find the mean and the standard deviation of this distribution.

4.What is the probability that at exactly 140 respondents report they text and drive?

5.What is the probability that at most 140 respondents report they text and drive?

6.What is the probability that at least 140 respondents report they text and drive?