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

(1 point) What is the probability that the second unbelted driver is in the ninth car stopped?

(1 point) What is the probability that of the first 10 drivers, 8 or more are wearing their seatbelts?

(1 point) 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?

(1 point) If they stop 120 cars during this safety check, what is the probability they find at least 12 drivers not wearing seatbelts?

Answer #1

Thank you.

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...

Assume that police estimate that 18% of drivers do not wear
their seatbelts. They set up a safety roadblock, stopping cars to
check for seatbelt use. They stop 40 cars during the first hour. a.
Find the mean, variance, and standard deviation of the number of
drivers expected not to be wearing seatbelts. Use the fact that the
mean of a geometric distribution is mu equals StartFraction 1 Over
p EndFraction and the variance is sigma squared equals
StartFraction q...

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