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.

d. Using the criteria summarized in Figure 3-6, is the commute time of 95 minutes significantly low, significantly high, or neither?

Accepted Answer

Below 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. The recorded daily screen time usage and units of minutes for a group of individuals is analyzed. Among the 800 recorded times, the mean is 320.5 minutes with a standard deviation of 85.3 minutes. Given a screen time usage of 500 minutes, is this value considered significantly low, significantly high, or neither? Awesome. So it appears for this particular problem we're trying to determine whether or not a provided screen time usage of 500 minutes is considered significantly low, significantly high, or neither, provided all the conditions set to us by the prom itself. So with that said, now that we know 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 significantly low, B is significantly high, and C is neither significantly low nor high. Awesome. So our first step that we need to take in order to solve this particular problem is we need to write down all of our given or all of our known variables. So let us note that our recorded screen time usage time, which we'll call X, is equal to 500 minutes. And let us note that we're told that the mean screen time usage, which we'll call mu, is equal to 320.5 minutes. We're also told the standard deviation, which we'll call sigma, and sigma is equal to 85.3. Minutes, fantastic. So now, our second step that we need to take is we need to recall and use the difference equation to help us compute the difference value. So let us know that the difference D is equal to X minus mu, which will be equal to 500 minus 320.5, which will be equal to implementer calculator, 179.5 minutes. And now that we've solved for our difference, our third step is we need to solve for the Z score. So as we should recall a note, the equation to solved for the the Z score states that Z is equal to X minus mu, which is the difference, divided by sigma, which is the standard deviation. So this will be equal to 179.5 divided by. 85.3, which will be equal to 2.10. Fantastic. And our 4th and final step is we need to interpret our Z score answer. So with that said, as we should recall a note, In standard normal distribution, a value is considered significantly high if the Z score is greater than or equal to 2.00. So with that said, a value is considered significantly low if Z is less than or equal to 2.00. So, therefore, if -2.00 is less than or equal to Z and Z is less than or equal to 2.00, that will mean that as a result, The value will be considered neither significantly high nor low. So let's say, let's state that again. So, if -2.00 is greater than or equal to Z and Z is less than or equal to 2.00, then that will mean that the value is considered neither significantly high nor low. And since our calculated Z score is 2.10, which is slightly greater than 2.00, that will mean that 500 minutes is considered significantly high, which I'll call SH for short, so it's significantly high, and that is our final answer. Hooray, we did it. So that means our final answer without a doubt has to be multiple choice answer letter B, which is significantly high. 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 Scores

Mean and Standard Deviation

Significance in Statistics

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