Problem

The average commute to work (one way) is 25 minut…

04:51

Problem 9 Medium Difficulty

The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. What is the probability that the vehicle was driven more than 15,000 miles? Less than 8000 miles? Would you buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year?

Answer

0.0262; 0.0003; would want to know why it had only been
driven less than 6000 miles (TI: 0.0260; 0.0002)

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Intro Stats / AP Statistics

Elementary Statistics a Step by Step Approach

Chapter 6

The Normal Distribution

Section 2

Applications of the Normal Distribution

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Video Transcript

Okay, So in this problem were asked to find the probability that the vehicle is driven more than 15 dozen miles. We can read that probability X greater 15 1000. We know that from the problem that mean is equal to 12,494 94 on the standard deviation is equal to 1002 190. Now, given these pieces of information and the fact that this data is normally distributed, you can use the formula X minus mu over. Signal is you got to see. So we're just gonna go ahead and do that for this number like that in its X 15,000 I was 12,490 for over. This is over 1290 is equal to 1.94 on. If you look at our see table that has a correspondent, probability is your point nine seven 38 Okay, now we're going to be right this in terms of dizzy value, because that's what we have here. And then input the probability to get our final answer. So figure I didn't do that. We get probability. Let's see. Was created 1.94 is equal to one minus a property. Z is less than 1.94 which is equal to one minus 0.97 three A. Just go to is your appoints your 262 If you look Gettinto, go later. Now, the second part of this question is asking us, Teoh find the Probably that the car has driven less than 800 months. It doesn't anise and aid does. And so to do this, we're gonna, um, find the Z value of Z score value for 8000 1000 minus, uh, 12 dozen for 94 over 1002 190 center deviation. We're gonna get Dingell three point for eight. This is a corresponding Bilgi. Loves your 251 I believe. Choose your zero. That is her phone lunch. Because this is less than so. You don't have to rearrange it. The first part of the problem Now the final part of this problem is asking, um, would you buy a vehicle if you've been told had been driven less than 6000 miles in the past year. And so we're just gonna find the probability that car trip in less than 6000 Nos. And to do that, we're gonna I need to do is find a Z value 6000 finest Wilson for for 90 90 for over was it doesn't told her. 90 1002 119. That's gonna give us negative sides. Sure, three for which has, of course, my brother gives you, which is very, very small. One very small.

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