A customer service desk with 1 worker is able to process an average of 8 customer inquiries per hour. An average of 4 customers arrive for help at the desk each hour. 1. What is the probability that 2 customers will arrive in the next hour? 2. What is the probability it will take longer than 11 minutes to serve a customer? 3. What is the average time required to serve a customer (in minutes)? 4. What is the probability that more than 2 customers will arrive in the next hour? HINT: P(X>2) = P(X=3) + P(X=4) +... + P(X=?) Remember: ????? P(X = k) = 1.0 Therefore: P(X>2) = 1.0 - ?Ā²??? P(X = k)
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The probability that 2 customers will arrive in the next hour: This is a Poisson distribution problem with Ī» = 4 (average number of customers arriving per hour). We want to find the probability that X = 2. P(X = 2) = (e^(-Ī») * (Ī»^X)) / X! P(X = 2) = (e^(-4) * Show moreā¦
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