Question

You walk to the bus stop not knowing when the next bus will come. the time you have to wait follows a uniform distribution from 0 to 7 minutes. what proportion of the time will you have to wait less than one minute or more than five minutes for the bus to come?

(a) 0.5714
(b) 0.1892
(c) 0.4286
(d) 0.2857
(e) 0.3640

Answer 1

To find the proportion of the time you have to wait less than one minute or more than five minutes for the bus to come, you need to find the cumulative probability of waiting less than one minute and more than five minutes. The proportion is approximately 0.4286. Option c

Step-by-step explanation:

To find the proportion of the time you have to wait less than one minute or more than five minutes for the bus to come, you need to find the cumulative probability of waiting less than one minute and the cumulative probability of waiting more than five minutes.

Since the time you have to wait follows a uniform distribution from 0 to 7 minutes, the probability of waiting less than one minute is the ratio of the length of the interval from 0 to 1 minute to the length of the whole interval from 0 to 7 minutes. Therefore, the probability is 1/7.

The probability of waiting more than five minutes is the ratio of the length of the interval from 5 to 7 minutes to the length of the whole interval from 0 to 7 minutes. Therefore, the probability is 2/7.

To find the proportion of the time you have to wait less than one minute or more than five minutes, you add the probabilities of waiting less than one minute and waiting more than five minutes. Therefore, the proportion is 1/7 + 2/7 = 3/7, which is approximately 0.4286. Option c