Question

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. (Use R where necessary)

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

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

3. What is the probability that of the first 10 drivers, 8 or more are wearing their seatbelts?

4. If they stop 30 cars during the first hour, find the mean and standard deviation of the number of drivers not expected to be wearing seatbelts?

5. If they stop 120 cars during this safety check, what is the probability they find at least 12 drivers not wearing seatbelts?

Answer 1

Answer:-

Given That:-

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

(a)Let X: No of drivers to be stopped to get first drivers without seat belt bucked .

  

(b) undefined driver is in the car stopped)

=P(exactly 1 unbelted is 8 cars stopped )p( car stopped had driver unbelted)

(c) P(8 or more wearing seat belt in first 10)

=P(x=8 or 9 or 10) here X: No .of driver wearing

seat belt out of 10.

(d)X:No .of driver who didn't wear seat belt

(e) X: No .of drivers who didn't wear seat belt in 120.