MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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  1. Federal law under Title 49 of the United States Code, Chapter 301, Motor Vehicle Safety Standard took effect on January 1, 1968 and required all vehicles (except buses) to be fitted with seat belts in all designated seating positions. While most states have laws requiring seat belt use today, some people still do not “buckle up.”  Let’s assume that 90 % of drivers do “buckle up.”  If drivers are randomly stopped to check seat belt usage, answer the following questions and show your work.

 

  1. How many drivers do they expect to stop before finding a driver whose seatbelt is not buckled?

 

  1. What is the probability that the second unbelted driver is in the ninth car stopped?

 

  1.  What is the probability that of the first 10 drivers, 8 or more are wearing their seatbelts?
Expert Solution
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Step 1

Given that 90% of drivers buckled up(wear seat belt).

The percentage of drivers without seat belt is,= 100%-90%=10%=10/100=0.10

Let the random variable x be the number of cars stopped to get the first driver without Seat belt.

The probability of success is considered as the percentage of drivers without seat belt. That is, p= 0.10

Here x follows geometric distribution with parameter p=0.10.

Therefore, the expected number of drivers to stop before finding a driver whose seatbelt is not buckled is ,

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