   Chapter 8.4, Problem 44E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Budgeting The amount spent monthly, x, for maintenance and repairs at XONIX, LLC, is normally distributed with a mean of $250 and standard deviation of$30. If x is the amount budgeted for next month, find x so that the probability of being overbudget for maintenance and repairs is 0.05.

To determine

To calculate: The budget so that probability of being over-budget for maintenance and repairs is 0.05 if the amount spent monthly, x, for maintenance and repairs at XONIX, LLC, is normally distributed with a mean of $250 and standard deviation of$30.

Explanation

Given Information:

The amount spent monthly, x, for maintenance and repairs at XONIX, LLC, is normally distributed with a mean of $250 and standard deviation of$30.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

The probability here is normally distributed and the mean and standard deviation is as follows:

μ=250σ=30

Now to find x so that the probability of being over budget for maintenance and repairs is 0.05 that is,

Pr(zxμσ)=0.051Pr(zxμσ)=0

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