### Reducing Personal Call Expenses with a New Phone System**Introduction**A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $400 per month and a standard deviation of $50 per month.**Explanation**To understand the data, refer to such expenses as PCE’s (personal call expenses). Find the point in the distribution below which 2.5% of the PCE’s fell.**Details to Calculate**- **Mean (μ)**: $400 per month- **Standard Deviation (σ)**: $50 per month- **Distribution Type**: Normal Distribution**Calculation for the 2.5% Threshold**For a normal distribution, the point below which 2.5% of the values fall corresponds to approximately -1.96 standard deviations from the mean (using Z-scores).**Formula:**\[ X = \mu + Z \times \sigma \]Where:- $ \mu $ is the mean,- $ Z $ is the Z-score,- $ \sigma $ is the standard deviation,- $ X $ is the value to find.**Applying Values:**\[ X = 400 + (-1.96) \times 50 \]\[ X = 400 - 98 \]\[ X = 302 \]Therefore, below $302 is the point where 2.5% of personal call expenses fall under the previous phone system. This insight is crucial in understanding the behavior of personal call expenses and to gauge the effectiveness post-implementation of the new system.

From the given information we want to find the point in the distribution below which 2.5% of the…

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $400 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the point in the distribution below which 2.5% of the PCE's fell.

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $400 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the point in the distribution below which 2.5% of the PCE's fell.

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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