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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 $95,000 \mathrm{km}$ and $115,000 \mathrm{km} ?$

Intro Stats / AP Statistics

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

Descriptive Statistics

University of North Carolina at Chapel Hill

Piedmont College

Oregon State University

University of St. Thomas

Lectures

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07:46

The mean lifetime of a cer…

02:42

Lifetime of a tire Assume …

03:44

A particular brand of tire…

05:41

The mean number of miles d…

03:45

For Exercises $5-8,$ use t…

01:57

A car manufacturer claims …

05:45

00:56

A natural gas utility is c…

00:50

Use the following informat…

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Welcome to numerous in the current problem. We are considering the lifetimes of tigers, Which is distributed normally between 10 to 10, uh relax kilometer and sorry, one like kilometer and sigma to be 10,000 kilometers. Now we are asked the question that what percentage of tires will last between 95,000 km, 2, 1, these many kilometers. So for that the first thing that we will start is funded rising. So we will have 95 triple zero minus 1, 2, 3, 4, 5, less than x minus late, Less than 115 000 -100000 divided by 10,000. Now this after being simplified, it will become minus this, correct? Because 100 minus 95 is five and 33 zeros and then less than this will be zed and this will be 15,000 divided by 10,000, which will give -0.5, less than zero, Less than 1.5. That is if there is a Standard normal distribution like this centered at zero. So this is something -0.5 and this is something say one. So this will be 1.5. So we want to know what percent will be this. So what we will do, we will take the entire area left to this, that is this, and then take the entire area left to this. And then we will find that probability Some probability said less than 1.5 Minour probability of zero, less than -0.5, Which is equivalent to probabilities said less than 1.5. This stays common but this becomes zero, greater than 0.5. Due to symmetry of normal distribution, which will be probability zed less than 1.5 -1 minus probability that less than 0.5. This is because the regular table, Yes, the regular table table that we have this will generally be giving the area less than if you can get a table that gives the value more than this. And you can directly that evaluate this. Now, going back to the values probabilities hit less than 1.5. years over here. So this is the value we are considering 0.9332 -1 plus. Probably to sit less than 0.5. So which is this? So it is 0.6915 6915. So how much will this value? B let us calculate. So For that I will simply use Excel. So I have a point line 33. Cool .9 metric -1 plus .6915. Eric. So we get 01 62 oh Little .6247. So we have 0.6247. Or if we do a percentage, it will be 62.47%. Right? So 62.47 percent. People will sort of tires Okay. This percent of tires will have a longevity of this.

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