Question 2) Waiting Line Analysis A customer service desk with 1 worker is able to process an average of 9 customer inquiries per hour. An average of 6 customers arrive for help at the desk each hour. a) What is the probability that 3 customers will arrive in the next hour?b) What is the probability it will take longer than 7 minutes to serve a customer? **Understanding Probability**In probability theory, the equation shown gives a hint on calculating the probability that a random variable \( X \) is greater than 2.### Hint:\[ P(X > 2) = P(X = 3) + P(X = 4) + \cdots + P(X = \infty) \]This equation means that the probability of \( X \) being greater than 2 is the sum of the probabilities of \( X \) being equal to 3, 4, and so on, up to infinity.### Key Concept:**Recall that**\[ \sum_{k=0}^{\infty} P(X = k) = 1.0 \]This indicates that the sum of the probabilities of all possible values \( X \) can take on (from 0 to infinity) is equal to 1, representing the certainty that \( X \) will take on some value.### Therefore:\[ P(X > 2) = 1.0 - \sum_{k=0}^{2} P(X = k) \]By this step, we understand that the probability of \( X \) being greater than 2 is equal to 1 minus the sum of the probabilities of \( X \) being 0, 1, or 2. This relation helps in simplifying the calculation of probabilities for values greater than a certain threshold by subtracting the sum of probabilities of other known values from 1.By understanding these steps, students can effectively compute and analyze probabilities for ranges and intervals of random variables.

Name: Question 2) Waiting Line Analysis A customer service desk with 1 worke
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Question 2) Waiting Line Analysis A customer service desk with 1 worker is able to process an average of 9 customer inquiries per hour. An average of 6 customers arrive for help at the desk each hour. a) What is the probability that 3 customers will