Point 2. An authorized virtual store of a well-known cellphone brand is interested in understanding and improving the customer service experience through its digital channels. For the store owners, the live chat communication channel is fundamental, for which they have assigned a small team to exclusively attend this channel. One of the key performance indicators of efficient communication and good customer service is the response time to the first message, that is, the time that elapses from when a user starts a chat conversation until any service agent responds to the customer. Class Exercises The goal for the service agents is that this time be less than a minute, but for various reasons, a customer does not always receive a prompt response. If this time exceeds five minutes, an automatic message is sent asking the customer to try communicating later. One of the store's data analysts has found that the time for the first response, in minutes, can be represented as a random variable X with the following probability density function: 0 < x <1 fx(x)= 12 0 otherwise a. Graph the Probability Density Function fx(x) of the random variable X. b. Find and graph the Cumulative Distribution Function Fx(x) of the random variable X. c. Using the Cumulative Distribution Function Fx (x), found in the previous part, calculate the probability that the response time to a chat request selected at random is between 0.8 minutes and 1.6 minutes.

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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Transcribed Image Text:Point 2. An authorized virtual store of a well-known cellphone brand is interested in understanding and improving the customer service experience through its digital channels. For the store owners, the live chat communication channel is fundamental, for which they have assigned a small team to exclusively attend this channel. One of the key performance indicators of efficient communication and good customer service is the response time to the first message, that is, the time that elapses from when a user starts a chat conversation until any service agent responds to the customer. Class Exercises The goal for the service agents is that this time be less than a minute, but for various reasons, a customer does not always receive a prompt response. If this time exceeds five minutes, an automatic message is sent asking the customer to try communicating later. One of the store's data analysts has found that the time for the first response, in minutes, can be represented as a random variable X with the following probability density function: 0 < x <1 fx(x)= 12 0 otherwise a. Graph the Probability Density Function fx(x) of the random variable X. b. Find and graph the Cumulative Distribution Function Fx(x) of the random variable X. c. Using the Cumulative Distribution Function Fx (x), found in the previous part, calculate the probability that the response time to a chat request selected at random is between 0.8 minutes and 1.6 minutes.

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