Find each probability using the standard normal distribution.

Question

b. P(z < 2.23)

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. Determine the probability that a standard normal variable Z is less than -1.15. Awesome. So it appears for this particular prompt we're asked to determine the probability that a standard normal variable Z is less than -1.15. So now that we know what we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is 0.9749. B is 0.5251, C is 0.1251, and D is 0.1621. Awesome. So, first off, as we should recall a note, we need to note once again that we're trying to find the probability that the standard normal variable Z is less than One, so we need to note that Z in this case, as the problem tells us, that Z is less than -1.15. So once again we're trying to find the probability that a standard normal variable Z is less than -1.15. So that means we're trying to find the probability P of Z is less than -1.15. Fantastic. So, with that in mind, we need to look up our Z table in our textbook or use a calculator, so we need to once again recall that we need to Look up in our textbook a Z table or to use our calculator. So we're trying to look up the cumulative probability for Z is equal to -1.15. And when we do that, we will find that P of Z is less than -1.15 is equal to 0.1251, and that is our final answer. Hooray, we did it, and this corresponds to multiple choice answer letter C, which once again is 0.1251. And that's it. 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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Find each probability using the standard normal distribution.

b. P(z < 2.23)

Key Concepts

Standard Normal Distribution

Z-Score

Cumulative Distribution Function (CDF)

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Find each probability using the standard normal distribution.b. P(z < 2.23)