z Scores. In Exercises 5–8, express all z scores with two deci...

Question

z Scores. In Exercises 5–8, express all z scores with two decimal places.

New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.

c. Convert the commute time of 95.0 minutes to a z score.

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. The recorded daily screen time usage in units of minutes for a group of individuals is analyzed. Among the 950 recorded times. The mean is 425.5 minutes with a standard deviation of 75.3 minutes. Given a screen time usage of 600 minutes, convert this time into a Z score. Awesome. So it appears for this particular problem we're ultimately trying to take our screen time usage value of 600 minutes, and we're converting this time into a Z score based on all the information that was provided to us by this problem. So with that said, now that we know what we're ultimately trying to solve for, let us read off our multiple choice answers to see what our final answer might be. A is 2.32, B is 3.35, C is 3.79, and D is 4.13. Awesome. So our first step we need to take in order to solve this problem is we need to identify and write down all of our given variables. So let us note that our recorded screen usage time, which we'll call this X, and the value of X in this case is going to be equal to 600 minutes as we're told by the problem itself. And the mean screen time, which we'll call the mean mu, and mu will be equal to 425.5 minutes. We're also told the standard deviation, which will denote this as sigma, and sigma, the standard deviation is equal to 75.3 minutes. Fantastic. Our second step now is we need to recall the equation to help us compute the difference. So let us recall that the difference D is equal to x minus mu, which will be equal to 600 minus 425.5, which will be equal to 174.5 minutes. And now we need to use our value for the difference to help us calculate the Z score. So that's our third step is to solve for our final answer, the Z score. So let us recall and note that the Z score, which we'll call Z, is going to be equal to X minus mu, which is the difference, divided by sigma, which will be equal to 174.5 divided by. 75.3, which will be equal to when we plug that into our calculator. 2.317, which will mean that Z is approximately equal to 2.32 when we round to two decimal places, because as you can see, all of our multiple choice answers are rounded to two decimal places, so we have to round our answer to two decimal places. So that will, that's it. That would be our final answer. Hooray, we did it. So therefore, our final answer without a doubt has to be multiple choice answer letter A, which once again is 2.32. 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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Key Concepts

Z Score

Mean

Standard Deviation

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