Question

The Avin Secretariat Senvice procures temporacy office personnef for major corporations. They have found that 605 of their invices are paid within ten working days. A random sample of 19 invoices is checked. What is the probabaty that exactly 18 of the invoices will be paid within ten warking days? round your answer to four decimal places

Answer 1

To find the probability that exactly 18 of the invoices will be paid within ten working days, we'll use the binomial probability formula.

Step-by-step explanation:

To find the probability that exactly 18 of the invoices will be paid within ten working days, we'll use the binomial probability formula. The formula is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X=k) is the probability that X equals k,

C(n, k) is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial,

n is the number of trials.

In this case:

n = 19, k = 18, p = 0.605.

Using the formula and plugging in the values, we can calculate the probability as follows:

P(X=18) = C(19, 18) * 0.605^18 * (1-0.605)^(19-18)

Simplifying this expression, we get:

P(X=18) = 19 * 0.605^18 * (1-0.605)^1

P(X=18) = 19 * (0.605)^18 * (0.395)^1

Calculating this expression, we find that the probability that exactly 18 of the invoices will be paid within ten working days is approximately 0.0071.