Presidents Listed below are the ages (years) of presidents of ...

Question

Presidents Listed below are the ages (years) of presidents of the United States at the times of their first inaugurations (from Data Set 22 “Presidents” in Appendix B). Presidents who took office as a result of an assassination or resignation are not included. The data are current as of this writing. Use these ages to construct a frequency distribution. Use a class width of 5 years and begin with a lower class limit of 40 years. Do the ages appear to have a normal distribution?

A list of ages of U.S. presidents at their first inaugurations, ranging from 42 to 70 years.

Accepted Answer

All right. Hello, everyone. So this question says, listed below are the ages in years of Olympic marathon winners at the time of their victories. Use these ages to construct a frequency distribution. Use a class width of 5 years and begin with a lower class limit of 20 years. Do the ages appear to have normal distribution and give reason? And here we have the data set in question, which is the ages of Olympic marathon winners in years. As well as 4 different answer choices labeled A through D. So, in order to understand whether or not this data has a normal distribution or not, we first have to determine the class intervals. In this particular case, we're told to start at age 20. And use a class width of 5 years. From there we can create the intervals. The first one, for example, would be ages 20 to 24. Up next, you would have from 25 to 29. And then from 30 to 34. And then from 35 to 39. And so after that, Right, you would count for frequency. That is, you would count how many data values correspond to each class. And so for the given data set. The distribution is as follows. Two Olympic marathon winners were between the ages of 20 to 24. 13 were between the ages of 25 to 29. 11 were between the ages of 30 to 34. And 4 were between the ages of 35 to 39. And so with this distribution, let's talk about normality criteria. There are 3 factors to consider. The first one is symmetry. And in this particular case, the distribution is roughly symmetric with the most values concentrated in the middle, that is. The highest frequency. Of Olympic marathon winners are between the ages of 25 to 34, which represent the middle data values. The second factor to consider is unimodal shape. Now, the the term unimodal refers to the fact that there should be one single peak in the middle class intervals of the data. So that is the highest value should be in the middle, which is true in this case. Additionally, There should also be a gradual decrease. Right, because what that means is that the frequency should decline towards the extreme values, that is towards the lower and upper limits of the data set, which would align with the bell curve. Where the peak is towards the middle, as mentioned before. So in this particular case, all three criteria are true of the frequency distribution that we made from the given data set. So therefore, The ages do appear to follow a normal distribution. Which would make the correct answer option B the multiple choice. Which says, yes, the distribution is approximately normal because it is symmetric, unimodal, and bell shaped. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Frequency Distribution

Class Width

Normal Distribution

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