Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 2.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store,nj = 45 customers in the fırst line and n2 = 46 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. laces le o 00 74)

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...
icon
Related questions
Topic Video
Question

How do you solve. ref W9A2

Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 2.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, \( n_1 = 45 \) customers in the first line and \( n_2 = 46 \) customers in the second line. Find the probability that the difference between the mean service time for the shorter line \( \overline{X}_1 \) and the mean service time for the longer one \( \overline{X}_2 \) 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).

\[ P = \boxed{\hspace{20px}} \]
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 2.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, \( n_1 = 45 \) customers in the first line and \( n_2 = 46 \) customers in the second line. Find the probability that the difference between the mean service time for the shorter line \( \overline{X}_1 \) and the mean service time for the longer one \( \overline{X}_2 \) 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). \[ P = \boxed{\hspace{20px}} \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON