In Exercises 21–26, find the indicated probability using the s...

Question

In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(0.42 < z < 3.15)

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. Find the probability that the standard normal variable Z is between 0.34 and 2.98. Awesome. So it appears for this particular problem we're ultimately trying to figure out the probability that the standard normal variable Z is between 0.34 and 2.98. So now that we know that we're ultimately trying to solve for this probability value, let's read off our multiple choice answers to see what our final answer might be. A is 0.9986. B is 0.3655. C is 0.6331 and D is 0.2571. Awesome. So first off, what we need to do is we need to find the cumulative property for Z is equal to 2.98. So we need to look up the value of This particular one. So we're trying to find the value of this in our standard normal distribution table, which, as you should note, your standard normal distribution table, there should be one in your textbook. And when we use our standard normal distribution table, we could state that the probability P of Z is less than 2.98. will be approximately equal to 0.9986. Fantastic. We also need to find the cumulative probability for Z is equal to 0.34, and similarly, we need to look up the value in our standard normal distribution table, and when we do that, we will find that the probability P of Z is less than 0.34 will be approximately equal to 0.6331. So now our next step, as we should recall, is we need to subtract the two probabilities in order to find the probability that Z is between 0.34 and 2.98. So we need to take the probability P of 0.34 is less than Z and Z is less than 2.98. is equal to the probability of Z is less than 2.98 minus the probability P of Z is less than 0.34. So when we plug in our known variables, we will find that this is equal to 0.9986 minus 0.6331. Which when we plug this into our calculator and we round to 4 decial places to match all of our multiple choice answers, we will find that it's equal to 0.3655. And that's it. That is our final answer. Hooray, we did it. So therefore, without a doubt, the probability that the standard normal variable Z is between 0.34 and 2.98 is 0.3655, and this corresponds to multiple choice answer letter B, which once again is 0.3655. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

��app

In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(0.42 < z < 3.15)

Key Concepts

Standard Normal Distribution

Z-scores

Probability Calculation

Watch next

����app

In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.P(0.42 < z < 3.15)