Question

Taking the train According to New Jersey Transit, the $8:00\mathrm{A}.\mathrm{M}.$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 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 $2$or more of $6$days. Do not perform the simulation.

Short answer

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

Step-by-step solution

Given information

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

Explanation

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

$90\%=\frac{90}{100}=\frac{9}{10}$

• 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 $0$and $8$(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.