6.8 8.1 11.4 15.8 23.6 5 10 15 20 25 Thousands of Miles...

6.8 8.1 11.4 15.8 23.6 5 10 15 20 25 Thousands of Miles Driven Annually Q A researcher surveyed 507 adults and recorded the number of miles they drove their car in one year. The results are in the boxplot above and the annual number of miles is measured in 1000's. What is the range of the data values? thousand miles What is the maximum number of miles reported? thousand miles Twenty-five percent of the data are above what value? thousand miles Seventy-five percent of the data are above what value? thousand miles What percent of the data values are between 8.1 and 15.8? %

Transcript

00:01 A truck can be determined that the distance travel per truck is normally distributed with the mean of 30 ,000 and a standard deviation of 11 ,000.

00:09 We want to complete parts a through d below.

00:12 And it's talking about the proportion of trucks expected to travel between different intervals of miles.

00:18 So what we need to do is find the z score for each one of these.

00:22 So i've kind of listed all that out.

00:24 And from reading the problem, i see down at the bottom, it wants us to repeat it for standard deviation of 8.

00:30 So what i'm going to do is find the z scores for each one of these values for 11 and for 8.

00:37 The formula for our z score is x our value minus the mean over the standard deviation.

00:43 So let me write that for the first one.

00:45 That's going to be our value which is 17 minus our mean which is 30 over a standard deviation of 11.

00:52 And then for the second one we do the same thing is that 17 minus 30 over 8.

00:59 That's going to give us our individual z scores.

01:02 I'm going to do that for each one of the values that are given here and find the z scores for 11 and 8.

01:10 I'm going to pause the video while i do that.

01:13 So i found each one of the z scores, and i want to start by doing the black z scores where the standard deviation is 11.

01:20 So let's understand what this means here.

01:22 We have our normal distribution.

01:24 We have our mean of 30.

01:26 We have a standard deviation of 11, and we want to know the number of trucks that are between 17 and 30 ,000 miles.

01:34 So we need here's 17 and here's 30.

01:37 So we need to know that proportion is going to be this area here.

01:42 And we do that by finding the values in our z score table and then and get what that will help us to find that area.

01:52 When we're looking at the next one, we want to know between 15 and 40.

01:57 So i'm going to be finding my value of 40, which is, excuse me, over here, and i would be finding the green area to get our proportion.

02:09 So now we need to find the corresponding values to the z scores on our table.

02:15 Now, i can't pull up a z score table on the screen, but there are two different tables, one for negative z values and one for positive z values.

02:27 So for those z, on that table, you need to be able to read that.

02:31 So the first one, we have a negative z value.

02:33 So i want to go to my negative z value table, and i want to find negative 1.

02:43 When i look that up, i get a value on that table of being 0 .0301.

02:48 So you need to make sure that you can look at your table and get that particular value.

02:54 So i'm going to go ahead and get all the z values in from the table...

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