Finding Probability In Exercises 47–56, find the indicated pro...

Question

Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(- 0.89 < z < 0)

Accepted Answer

Welcome back, everyone. Using the standard normal distribution, find the probability that Z is between negative 0.45 and 0. A says it's 0.2266. B 0.1736, C 0.3264, and D 0.5000. Now how can we figure out this probability? Well, remember that the standard normal distribution is a bell-shaped curve that is symmetric above the mean mu equals 0 and has a standard deviation sigma of 1, OK? So here this would be our curve, right? And now a Z score represents how many standard deviations a value is from the mean. So, for example, when we say the probability that Z is less than 0, then we would look for the area under the curve to the left of a Z score of 0, OK? So now, in our table, well, we can tell from the diagram, but if we were also to use that Z table, OK, from the Z table. Then we can tell that the probability that Z is less than 0 would be equal to 0.5, 000. And that makes sense because that is one half of the graph, one side of the graph, OK? Now if we think about it. If we're looking for the probability that Z is less than -0.45, we can also get it from our table. And if we were to put this on our normal distribution. If all of this area is the probability that Z is less than 0, OK. And then if this other area, the second area I'm gonna shade in blue is the probability that Z is less than 0.45 sigma, OK? Then that means this remaining area would be the probability that Z is between -0.45 and 0, OK? So this tells us then. OK, that the probability that Z is between negative 0.45 and 0. Is going to be equal to the probability that Z is less than 0 minus the probability that Z is less than 0. 0.45. No, I, I just did that as a segue to show you where we're eventually heading. OK. So let's put that probability Z is between negative 0.45 and 0. And we've essentially solved the first part of this problem. We know what the probability that Z is less than 0 is. It's 0.5 000. So now, we need to go back to our Z table and find the probability that Z is less than -0.45. Now when we look at our table, that probability would be 0.3264. So no, that means this probability will be 0.5000 minus 0.3264. Which would be equal to 0.1736? Thus, the probability that Z is between negative 0.45 and 0 is 0.1736 or answer choice B. Thanks a lot for watching everyone. I hope this video helped.

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Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(- 0.89 < z < 0)

Key Concepts

Standard Normal Distribution

Z-Scores

Probability Calculation

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Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.P(- 0.89 < z < 0)