Question

The National Occupant Protection Use Survey (NOPUS) was conducted to provide probability-based data on motorcycle helmet use in the United States. The survey was conducted by sending observers to randomly selected roadway sites where they collected data on motorcycle helmet use, including the number of motorcyclists wearing a Department of Transportation (DOT)-compliant helmet (National Highway Traffic Safety Administration website, January 7, 2010). Sample data consistent with the most recent NOPUS are shown below.

The National Occupant Protection Use Survey (NOPUS) was conducted to provide probability-based data on motorcycle helmet use in the United States. The survey was conducted by sending observers to randomly selected roadway sites where they collected data on motorcycle helmet use, including the number of motorcyclists wearing a Department of Transportation (DOT)-compliant helmet (National Highway Traffic Safety Administration website, January 7, 2010). Sample data consistent with the most recent NOPUS are shown below.The National Occupant Protection Use Survey (NOPUSa. Use the data to compute the probability that a motorcyclist wears a DOT-compliant helmet. Round your answer to four decimal places.b. The probability that a motorcyclist wore a DOT-compliant helmet five years ago was 0.48, and last year this probability was 0.63. Would the National Highway Traffic Safety Administration be pleased with the most recent survey results shown above?c. What is the probability of DOT-compliant helmet use by region of the country? Round your answer to four decimal places. Northeast: Midwest: South:West:

a. Use the data to compute the probability that a motorcyclist wears a DOT-compliant helmet. Round your answer to four decimal places.

b. The probability that a motorcyclist wore a DOT-compliant helmet five years ago was 0.48, and last year this probability was 0.63. Would the National Highway Traffic Safety Administration be pleased with the most recent survey results shown above?

c. What is the probability of DOT-compliant helmet use by region of the country? Round your answer to four decimal places.

Northeast:
Midwest:
South:
West:

Answer 1

Concepts and reason

The concept of probability is used here to determine the probability.

The probability can be defined as a measure of likelihood that an event will occur. The probability will lies between 0 and 1 where o implies the impossibility of the occurrence of the event and 1 implies that the event will certainly occur where the outcomes of the random experiment consider as event.

Fundamentals

The probability of an event can be calculated as:

(a)

The total number of motorcyclist is $(350+170)=520 $ and among them there are 350 motor cyclist who wear a DOT-compliant helmet.

So, the probability that a motorcyclist wears a DOT-compliant helmet is calculated as:

(b)

The probability that motorcyclist wore a DOT-compliant helmet five years ago was 0.48 and last year the probability was 0.63. According to the recent study the probability that a motorcyclist wears a DOT-compliant helmet is 0.6731.

It shows an increase in the probability that a motorcyclist wears a DOT-compliant helmet. So, the National Highway Traffic Safety Administration should be pleased with the recent survey results.

(c)

The total number of motorcyclist who wear the helmet in each region is the total number of possible cases and the number of motorcyclist who wear the DOT-complaint helmet is the number of favorable cases in each region.

The probability of DOT-complaint helmet use by each region of the country is calculated and shown in the table below:

Ans: Part a

The probability that a motorcyclist wears a DOT-compliant helmet is 0.6731.

Part b

Yes, the National Highway Traffic Safety Administration should be pleased with the recent survey results as there in an increase in the probability.

Part c

The probability of DOT-complaint helmet use by Northeast, Midwest, South, and West of the country are respectively.