**Probability Distribution of Customer Service Telephone Lines**A business has six customer service telephone lines. Let $ x $ denote the number of lines in use at any given time. Suppose that the probability distribution of $ x $ is as follows:| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 ||----|-----|-----|-----|-----|-----|-----|-----|| p(x) | 0.05 | 0.10 | 0.18 | 0.39 | 0.18 | 0.08 | 0.02 |**Events and Probability Calculations**Write each of the following events in terms of $ x $, and then calculate the probability of each one.(a) **At most three lines are in use**: Event: $ x \leq 3 $ \[ P(x \leq 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) \] \[ = 0.05 + 0.10 + 0.18 + 0.39 = 0.72 \](b) **Fewer than three lines are in use**: Event: $ x < 3 $ \[ P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) \] \[ = 0.05 + 0.10 + 0.18 = 0.33 \](c) **At least three lines are in use**: Event: $ x \geq 3 $ \[ P(x \geq 3) = P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) \] \[ = 0.39 + 0.18 + 0.08 + 0.02 = 0.67 \](d) **Between two and five lines (inclusive) are in use**: Event: $ 2 \leq x \leq 5 $ \[ P(2 \leq x \

As per our guidelines we are suppose to answer only three sub parts. Required probability is P(X≤3)

Answered: A Business has six customer service…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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