Q. 20 Taking the train According to Ne... [FREE SOLUTION]

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 5: Q. 20 (page 311)

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 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.

Expert verified

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

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

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.