Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company’s claim isn’t true? Design and carry out a simulation to answer this question. Follow the four-step process.

The claim that there is a chance $90\%$that the train will arrive on schedule. Over the course of a month, a sample of arrival times is taken on $6$random weekdays. The following is the time of the train's arrival based on the sample taken: $1-\frac{2}{6}=\frac{4}{6}=66.6\%$

$0$We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between (never happens) and $1$ (happens frequently) (always occurs).

We should, in order to simulate, Use two-digit numbers instead of three-digit numbers. The train is on time if the numbers $00$to $89$are used. Allow the numbers $90$to $99$to symbolise the train's lateness. Pick six numbers at random, with no repeat permitted. Count how many times the train has been late. Rep this simulation as many times as you like. You will most likely get a report indicating that the train is running late between $0$ and $2$ times. As a result, they lack persuasive evidence that the company's claim is false.