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Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 21 customers in the first line and n₂ = 28 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X, and the mean service time for the longer one X₂ is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables.

Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 21 customers in the first line and n₂ = 28 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X, and the mean service time for the longer one X₂ is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 21 customers in the first line and n₂ = 28 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i
Transcribed Image Text:Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 21 customers in the first line and n₂ = 28 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i
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