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Chapter 5: Q. 20 (page 311)

Taking the train According to New Jersey Transit, the 8:00A.M.weekday train from Princeton to New York City has a 90%chance of arriving on time. To test this claim, an auditor chooses 6weekdays at random during a month to ride this train. The train arrives late on 2of those days. Does the auditor have convincing evidence that the company's claim is false? Describe how you would carry out a simulation to estimate the probability that a train with a 90%chance of arriving on time each day would be late on 2or more of 6days. Do not perform the simulation.

Short Answer

Expert verified

The train arrives on time only if the number is between 0and 8otherwise the train will not arrive on time.

Step by step solution

01

Given information

W need to find out the probability that train will arrive on time or not.

02

Explanation

The train has a 90%chance of arriving on time, which translates to around 9out of every 10days.

90%=90100=910

  • Using slips of paper, a random digits table, or a random number generator, produce digits at random.
  • The first digit should be chosen. If the number is between 0and 8(inclusive), the train will arrive on time; otherwise, it will be late.
  • Repeat until we have a result for six days, and then count how many times the train is late throughout those six days.
  • Repeat as many times as necessary, estimating the probability as the proportion of trials with two or more days of lateness among the six days.

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Most popular questions from this chapter

Color-blind men About 7% of men in the United States have some form of red-green color blindness. Suppose we randomly select one U.S. adult male at a time until we find one who is red-green color-blind. Should we be surprised if it takes us 20 or more men? Describe how you would carry out a simulation to estimate the probability that we would have to randomly select 20 or more U.S. adult males to find one who is red-green color blind. Do not perform the simulation.

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