In Exercises 7–18, find the indicated area under the standard ...

Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.5 and to the right of z = 1.5

Accepted Answer

Below there today we're going to 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. Find the area under the standard normal curve that lies to the left of Z equals -2.1 and to the right of Z equals 2.1. Awesome. So it appears for this particular problem we're ultimately trying to determine the area under the standard normal curve that lies to the left of Z equals -2.1 and to the right of positive Z equals 2.1. Awesome. So now that we know we're ultimately trying to solve for this area value, let's read off our multiple choice answers to see what our final answer might be. A is 0.0358. B is 0.9642. C is 0.0179 and D is 0.9821. Awesome. So first off, in order to solve this problem, let us make sure we understand what exactly we're being asked to solve for. So once again we're being asked to find the area under the standard normal curve to the left of Z equals -2.1 and to the right of Z equals 2.1. So with that in mind, we need to find the area to the left of Z equals -2.1, and when we use a standard normal distribution table, which you should have a standard normal distribution table in your textbook. So when we use that table, we will find that the area to the left of Z equals -2.1. will be approximately equal to 0.0179. And similarly, we need to find the area to the right of Z equals 2.1. So we also need to find the area to the right of Z equals 2.1, and using our standard normal distribution table, once again, we will determine that this is approximately equal to 0.0179. So now we need to add these two areas together, so the total area, which I'll call T subscript A, so the total area is equal to 0.0179 plus 0.0179. And when we plug that into our calculator, you will find that it's equal to 0.0358. Fantastic. And that is our final answer. Hooray, we did it. So therefore, without a doubt, the area under the standard normal curve to the left of Z equals -2.1 and to the right of Z equals 2.1 is 0.0358. And this corresponds to multiple choice answer letter A, which once again is 0.0358. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.5 and to the right of z = 1.5

Key Concepts

Standard Normal Distribution

Z-scores

Area Under the Curve

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