Question

The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 60%

of their invoices are paid within ten working days. A random sample of 16
invoices is checked. What is the probability that fewer than 11
of the invoices will be paid within ten working days? Round your answer to the nearest ten-thousandth, if necessary.

Answer 1

The probability that fewer than 11 invoices will be paid within ten working days is 0.9999.

To solve this problem, we can use the binomial distribution formula:

P(X < 11) = Σ [nCx * p^x * (1-p)^(n-x)]

where:

X is the number of invoices paid within ten working days

n is the sample size (16)

p is the probability of an invoice being paid within ten working days (0.6)

nCx is the number of combinations of n things taken x at a time

We want to find the probability that fewer than 11 invoices will be paid within ten working days, so we need to sum the probabilities for X = 0 to X = 10.

Using a calculator or software, we can find that:

P(X < 11) = 0.9999 (rounded to four decimal places)

Therefore, the probability that fewer than 11 invoices will be paid within ten working days is 0.9999.