Question

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. Design and 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 of 6 days.- I am confused on how to do this it’s for a major grade with another problem using the R software.

Answer 1

To simulate the probability of a train being late 2 out of 6 days with a 90% on-time arrival rate, use a random number generator to represent 6 days. Run the simulation multiple times and calculate the proportion of trials with exactly 2 late arrivals to estimate the probability.

Step-by-step explanation:

To estimate the probability that a train with a 90% chance of arriving on time each day would be late on 2 of 6 days, you can use a simulation. Each trial of the simulation will represent a week with 6 days. Here's a step-by-step guide to design and carry out the simulation:

1. Decide on a method to simulate one day's result. You can use a random number generator where numbers 1 to 90 represent the train arriving on time, and 91 to 100 represent a late arrival.
2. Run the random number generator 6 times to simulate one week.
3. Count the number of times the result corresponds to a late arrival (numbers 91 to 100).
4. Repeat steps 2 and 3 many times (e.g., 1000 trials) to get a large enough sample size.
5. Calculate the proportion of trials where the train was late exactly 2 times out of 6. This proportion is an estimate of the probability you are looking for.

While this can be done manually or with a calculator, it would be much more efficient to perform this simulation using a computer program such as R.

Answer 2

We evaluate the probability like this:

`0.9^4*0.1^2`
the above value is a theoretical estimation, you have
to get the above value in your simulation, which equate:

`0,006561`