Question

The waiting time for a train has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this train is more than 4 minutes on a given day? Answer: (Round to two decimal place.)

Answer 1

To calculate the probability of waiting more than 4 minutes for a uniformly distributed train arrival time between 0 and 10 minutes, subtract 4 from 10 and divide by the total range of 10, giving a probability of 0.60 or 60%.

Step-by-step explanation:

The waiting time for a train with a uniform distribution means that any time within the range is equally likely. Since the total range is from 0 to 10, and we want to know the probability of waiting more than 4 minutes, we look at the interval from 4 to 10, which is 6 minutes out of the total 10 minutes.

Using the properties of uniform distribution:

Probability = (Favorable outcome) / (Total possible outcomes) = (10 - 4) / (10 - 0) = 0.6

So, the probability that the waiting time is more than 4 minutes is 6/10, which when rounded to two decimal places is:

0.60 or 60%

Answer 2

0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X higher than x is given by the following formula.

`P(X > x) = (b - x)/(b-a)`

The waiting time for a train has a uniform distribution between 0 and 10 minutes.

This means that
`a = 0, b = 10`

What is the probability that the waiting time for this train is more than 4 minutes on a given day?

`P(X > x) = (b - x)/(b-a)`

`P(X > 4) = (10 - 4)/(10 - 0) = 0.6`

0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day