Problem

Use the following data. The lifetimes of a certai…

Problem 17 Easy Difficulty

Use the following data. The lifetimes of a certain type of automobile tire have been found to be distributed normally with a mean lifetime of $100,000 \mathrm{km}$ and a standard deviation of $10,000 \mathrm{km}$ Answer the following questions.
What percent of the tires will last between $85,000 \mathrm{km}$ and $100,000 \mathrm{km} ?$

Answer

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Intro Stats / AP Statistics

Basic Technical Mathematics with Calculus

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

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Video Transcript

Welcome to memory. In the current problem. We are given the lifetimes the lifetimes of certain types of one years tires. Okay, so the sudden by himself touches lifetime most fires and we are also given that X follows a normal distribution with new equals one like kilometer, been lax kilometer and is equal to 10,000 no reliability. The question asking is what percentage? Well what is a bit of fires? What percentage of barriers between 85 1000 kilometers and then kilometers? Okay, then lack kilometers. So that is equivalent to asking this. Now, if we do a standardization, we get Divided by 10,000. Now, if we simplify this, we get probability now 100 -85 gives us 15, correct, This is it value and this is zero. So we will have -1.5, less than zero, less than zero. So in standard normal distribution like this, This will be zero And this will be -1.5, correct. Somewhere we're here. So, but what happens is we have 1.5 given over here that too this area completely. So the table gives okay, the table gives then less than area, correct. So this area. So what can we do? We want this area because this area and this area will be cool, correct. So we'll be right probability of That. Less than zero Minour probability of that is the -1 point faith, Correent. So probability of said less than zero Minour probability of zed greater than 1.5, which is equals two, probability zero, less than zero minus one minus probability zero less than 1.5. Because our table gives value less than that. So for 1.5 if I bring the diagram, little town, no 1.5 We have this value, correct? So we and for zero we have this value. It's we know already minus one plus zero point I don't want 9332, correct? So this and this will give 0.933 to minus 0.5 because 0.5 minus one is minus zero point right? So we get 0.4332 which Will be 43.32%. So 43.2% of all tires will have uh huh. Lifetime between 85,000 km two then black kilometers.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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