Question

Statistics from the Port Authority of New York and New Jersey show that 87% of the vehicles using the Lincoln Tuinset that connects New York City and New Jersey use E-ZPass to pay the toll other than stopping at a toll booth Twelve cats are randomly selected Click here for the Excel Data File o. How many of the 12 vehicles would you expect to use E Pass? (Round your answer to 4 decimal places.) Number of vehic b. What is the mode of the distribution? What is the probability associated with the mode? (Round your answer to decimal places Mode Probability

Answer 1

The expected number of vehicles using E-ZPass out of 12 is 10.4400. The mode of the distribution is 11, as it is the largest integer less than or equal to (12 + 1)(0.87). The exact probability of the mode requires further calculations using the binomial distribution formula.

Step-by-step explanation:

The student's question involves calculating expected values and probabilities using percentages in a real-world context. Specifically, the question deals with E-ZPass usage statistics and the expected number of vehicles that would use E-ZPass out of a sample.

To calculate the expected number of vehicles using E-ZPass out of 12 randomly selected cars, you would multiply the total number of cars by the probability of a car using E-ZPass. Since 87% of vehicles use E-ZPass, the expected number of vehicles using E-ZPass out of 12 would be:
12 vehicles * 0.87 = 10.44 vehicles. Rounded to four decimal places, the expected number is 10.4400.

As for the mode of the distribution, in a binomial distribution, the mode is the largest integer less than or equal to (n + 1)p, where 'n' is the number of trials and 'p' is the probability of success on any given trial.

In this case, 'n' is 12 and 'p' is 0.87, so the mode is the largest integer less than or equal to (12 + 1)(0.87), which is 11. However, calculating the exact probability associated with the mode requires a binomial distribution formula or technology such as a statistical calculator or software.