Miles Driven Annually The mean number of miles driven per...

Miles Driven Annually The mean number of miles driven per vehicle annually in the United States is 12,300 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1340 miles. Use The Standard Normal Distribution Table. Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places. (a) What is the probability that the vehicle was driven more than 15,000 miles? P(X > 15,000) = 0.0307 (b) What is the probability that the vehicle was driven less than 8000 miles? P(X < 8000) =

Transcript

00:01 We are looking at a normal distribution.

00:03 Let's start by drawing it.

00:05 The total area under this curve is 100%, and it is symmetric.

00:12 The mean is 12 ,500.

00:16 The standard deviation, 1 ,340.

00:20 Our first step is to find the probability a vehicle has driven more than 15 ,000.

00:26 Okay, so that's above the mean.

00:28 So we mark it on here.

00:30 We want this area up and all we can do is use the standard normal table.

00:35 So you do need something with the normal distribution built into it.

00:38 And they want us to use a table, so we'll do that.

00:41 We need the z score to put into that table.

00:44 A z score tells you how many standard deviations away from the mean a value is.

00:49 You find it by taking your value, subtracting the mean, dividing by the standard deviation.

00:56 So 15 ,000 minus 12 ,500, divide by 1 ,340, is 1 .87 to 2 decimal places.

01:05 If you look at the standard table, you have z scores on the rows and columns, areas in the middle.

01:11 But if we look for 1 .87, so you look for 1 .8, 0 .07, this isn't the area we're looking for.

01:18 The standard table gives you the area between z and 0, which is the mean of the standard normal curve.

01:25 So it gives me this area.

01:28 That's not what i want, but i know the normal curve is symmetric.

01:31 So the total area above the mean is 0 .5.

01:35 So i go from 0 .5, and i will subtract this area...

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