Using and Interpreting Concepts
Finding Area In Exercise...

Question

Using and Interpreting Concepts

Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.

dist

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A standard normal curve is shown below. Determine the area of the shaded region. Awesome. So it appears for this particular problem, we're asked to use our standard normal curve that is given to us by the problem itself. And we're asked to determine the area of the shaded region. So we're trying to find the area of the shaded region. So now that we know what we're trying to solve for, let's quickly read off our multiple choice answers to see what our final answer might be. So A is 0.1867, B is 0.2119, C is 0.7881. And D is 0.8133. Awesome. So looking at our curve really quickly to help us visualize what's happening, we have our curve represented by a solid blue curve. And our shaded region is shaded in baby blue, and it appears the shaded region ends at 0.8 and then continues going towards the right for our Z axis, it looks like. With 0 being where the peak is located on our curve. Awesome. So with that said, we need to note that a cumulative area to the right of Z is equal to -0.8. And this is given as the shaded region. We also need to recall and note that the table for the standard normal distribution typically shows the cumulative area to the left of a given score. Or rather, for specifically for the given Z score. So once again, this is really important to note. So the table for a standard normal distribution, which should be located in your textbook, typically shows the cumulative area to the left of a given Z score. So therefore, with that in mind, we need to subtract the cumulative area to the left of Z equals -0.8 from 1. In order to obtain the cumulative area to the right of Z equals -0.8. So using the table, From our textbook, we need to look at the intersection of row Z equals -0.8 and the column Z equals 0.00 because 0.8 plus 0.00 is equal to -0.8. Fantastic. So to keep things simple, I've gone ahead and took a screenshot from the textbook, essentially, and have our little table here. And looking at our table, looking at where they intersect, so if we follow our column negative 0.8 and we follow it over to the right to where our column 0.00 is, we will find that the intersection is at 0.2119. Awesome. So from the table, once again, the intersection is 0.2119, and this is the cumulative area to the left of Z equals -0.8. So therefore, without a doubt, the cumulative area to the right of Z equals 0.8 will be 1 minus 0.2119, which when you plug into our calculator, we will get 0.7881, and this will be our final answer. Hooray, we did it. And this corresponds to multiple choice answer letter C, which once again is 0.7881. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Using and Interpreting Concepts
Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.

Key Concepts

Standard Normal Distribution

Area Under the Curve

Z-Score

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Using and Interpreting ConceptsFinding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.