The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 40% of their invoices are paid within ten working days. A random sample of 12 invoices is checked. What is the probability that exactly 10 of the invoices will be paid within ten working days?

Answer:

Given :

The probability of success, $p=0.40$

The sample size, $n=12$

Solution :

→ The probability that exactly 10 of the invoices will be paid within ten working days :

$$P(x = 10) = \binom{n}{x} p^x (1 – p)^{n – x} \bigg|_{x=10}$$ $$= \binom{12}{10} 0.4^{10} (1 – 0.4)^{12 – 10}$$ $$= 0.002491$$

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