Question

The scheduled commuting time on the MTA Marc train from BWI to DC is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be less than 70 minutes

Answer 1

The probability that the commuting time will be less than 70 minutes is 0.6 or 60%.

Step-by-step explanation:

To find the probability that the commuting time will be less than 70 minutes, we need to determine the proportion of the total range of possible commuting times that is less than 70. Since the commuting time is uniformly distributed between 64 and 74 minutes, the range of possible commuting times is 74 - 64 = 10 minutes.

The proportion of commuting times less than 70 is then the difference between 70 and 64 divided by the total range of possible commuting times, which is 10.

So, the probability that the commuting time will be less than 70 minutes is (70 - 64) / 10 = 6/10 = 0.6 or 60%.

Answer 2

60% probability that the commuting time will be less than 70 minutes

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 lower than x is given by the following formula.

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

Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes.

This means that
`a = 64, b = 74`

What is the probability that the commuting time will be less than 70 minutes

`P(X < 70) = (70 - 64)/(74 - 64) = 0.6`

60% probability that the commuting time will be less than 70 minutes