On average, the drive-up window at Dann's Doughnuts serves 12 customers between 3:00pm and 4:00pm.

Question

On average, the drive-up window at Dann's Doughnuts serves 12 customers between 3:00pm and 4:00pm.

a) What is the probability of exactly 22 drive-up customers between 3:00pm and 4:00pm

[three decimal accuracy]

b) What is the probability of fewer than 22 drive-up customers between 3:00pm and 4:00pm

[three decimal accuracy]

c) What is the probability of at least 22 drive-up customers between 3:00pm and 4:00pm

[three decimal accuracy]

Answer 1

If we are using the "binomial distribution" again... which is consistent with other questions you asked, Peyton, then what is p = ? Is this a discrete situation, where the number of outcomes is a small finite number?

I'd say most likely yes, because the number of customers in an hour doesn't likely go above, say, 30.

When p is not given, we usually assume it is 0.5... especially given other hints in this problem. So let's assume p = 0.5. This means that the probability of 12 is right in the "middle" and P(13) = P(11). Symmetry, in other words.

Also, what does the "average" have to do with it?

And what do we use for n? (number of trials)?

Well it turns out that the average (mean) = n * p

So, that implies 12 = n * 0.5

Which means that "n" = 24.

So we have n = 24, and p = 0.5.

The meaning of the "22 customers" is P(x = 22) when the list of ALL outcomes (k) is 0 to 24

You can take it from here? Follow up with this thread if you get stuck ok?