On our quiz today, I came across the following question.
Assuming a telemarketer has a 20% chance of selling each caller an item, and a 80% chance of not selling the caller an item.
Each call in which the telemarketer makes a successful sale takes 2.5 minutes, and each call that doesn't sell takes 0.5 minutes. If the telemarketer makes 100 calls, find the average amount of time it takes.
I was conflicted between two methods.
Method 1: $E(Y)$ = (2.5)(0.2) + (0.5)(0.8) = 0.9, which I proceeded to multiply by 100 = 90 minutes.
Method 2: Since the question can be set up as a Bernoulli trial, $E(Y)$= $u$ = $np$. So 100(0.2)(2.5) = 50 minutes
I think either I misinterpreted the question, or I'm not doing something right. I feel I didn't set up the first method correctly, or if it's useable in this case.