On average, 19 passengers arrive at Harvard Square Station between 4:00am and 5:00am.

Question

On average, 19 passengers arrive at Harvard Square Station between 4:00am and 5:00am.

a) What is the probability of exactly 17 passengers arriving between 4:00am and 5:00am

[three decimal accuracy]

b) What is the probability of exactly 17 passengers arriving between 4:15am and 4:45am

[three decimal accuracy]

c) What is the probability of fewer than 17 passengers arriving between 4:15am and 4:45am

[three decimal accuracy]

d) What is the probability of at least 17 passengers arriving between 4:00am and 4:15am

[three decimal accuracy]

Answer 1

The time interval is relevant here. In addition to my previous help that I gave you, we also need to assume that the flow of passengers is "even" between 4 and 5 am.

If we change the time interval to 1/2 hour, then the "mean" will be 1/2 * 19

If the time interval is 3/4 hour, then the "mean" will be 3/4 * 19

And so on...

p = 0.5 (when not specified we assume that)

n = (mean) divided by 0.5

Proceed from there. You can do it.