Question

A temporary office personnel agency has determined 90% of the invoices they handle are paid on time. Suppose a sample of 12 invoices are selected:

What is the expected number of invoices that will be paid on time?

Answer 1

The expected number of invoices paid on time out of a sample of 12, when 90% are typically paid on time, is calculated using expected value and is 10.8. This means that typically, about 11 of the invoices will be paid on time.

Step-by-step explanation:

The student is asking about the expected number of invoices paid on time when it is known that 90% of the invoices the agency handles are paid on time. To calculate this, we use the concept of expected value in probability. For a sample of 12 invoices, where each invoice has a 90% chance of being paid on time, the expected number of invoices paid on time is found by multiplying the probability of an event by the number of trials:

Expected number = Probability of being paid on time × Number of invoices = 0.9 × 12 = 10.8

Therefore, the agency can expect that 10.8 out of 12 invoices will be paid on time, on average. Since we can't have a fraction of an invoice, in practice this means usually 10 or 11 invoices will be paid on time, with 11 being slightly more likely.