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Answer:
0.9942 = 99.42% probability that at least 6 of the invoices will be paid within ten working days
Step-by-step explanation:
For each invoice, there are only two possible outcomes. Either they are paid within 10 working days, or they are not. The probability of an invoice being paid within 10 working days is independent of other invoices. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
60% of their invoices are paid within ten working days.
This means that
A random sample of 18 invoices is checked.
This means that
What is the probability that at least 6 of the invoices will be paid within ten working days?
Either less than 6 are paid within 10 working days, or at least 6 are paid. The sum of the probabilities of these events is 1. So
We want . So
In which
Then
Finally
0.9942 = 99.42% probability that at least 6 of the invoices will be paid within ten working days