the alvin secretarial service procures temporary office personnel for major corporations. they have found that 50% of their invoices are paid within ten working days. a random sample of 12 invoices is checked. what is the probability that exactly 5 of the invoices will be paid within ten working days? round your answer to four decimal places.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Binomial Distribution" ], "new_concepts": [], "current_concepts": [ "Binomial Distribution", "Combinations" ] } ## Identify the probability distribution parameters Using the *Binomial Distribution* knowledge point $$ \begin{aligned} &n = 12\ &p = 0.50\ &q = 1 - p = 0.50\ &k = 5 \end{aligned} $$ ## Calculate the binomial probability Using the *Binomial Distribution* knowledge point $$ \begin{aligned} P(X = 5) &= \binom{12}{5} (0.50)^5 (0.50)^{12-5}\ &= \frac{12!}{5!(12-5)!} (0.50)^{12}\ &= 792 \times 0.000244140625\ &= 0.193359375 \end{aligned} $$ ## Round to four decimal places Using the *Binomial Distribution* knowledge point $$ P(X = 5) \approx 0.1934 $$ The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 50% of their invoices are paid within ten working days. A random sample of 12 invoices is checked. What is the probability that exactly 5 of the invoices will be paid within ten working days? Round your answer to four decimal places. 0.1934 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Distribution" ] }

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Explanation:

Identify the probability distribution parameters

Calculate the binomial probability

Round to four decimal places

Answer: