Comparing Values. In Exercises 13–16, use z scores to compare ...

Question

Comparing Values. In Exercises 13–16, use z scores to compare the given values.

Tallest and Shortest Men The tallest adult male was Robert Wadlow, and his height was 272 cm. The shortest adult male was Chandra Bahadur Dangi, and his height was 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is more extreme?

Accepted Answer

Welcome back, everyone. In this problem, the largest pumpkin ever recorded weighed 1190 kg, while the smallest commercially grown variety weighs about 0.45 kg. The average weight of pumpkins is 5.2 kg with a standard deviation of 1.8 kg. Use these scores to determine which of these two pumpkins has the weight that is more extreme. A says the largest pumpkin. B the smallest pumpkin. C. Both have the same extremity, and d neither is considered extreme. Now how can we use a Z score to determine which of these has the weight that is more extreme? What do we know about Z scores? Well, recall, OK, that the Z score, right, is equal to. The data point X minus the mean mu divided by the standard deviation sigma. Now, in this case, we are given two data points, 11,900 1190 kg and 0.45 kg, OK? So we could say that X1. Or rather not we, let me say given. X1 equals 1190 kg, and X2 equals 0.45 kg. We also know that the average meal is 5.2 kg and our standard deviation sigma is 1.8 kg. No, a Z score can tell us which is more extreme based on the absolute value. If the absolute value of the Z score is is higher, then it's the more extreme value. So let's find our Z scores and their absolute values, and that can tell tell us which one has a more extreme weight. Now, for our first Z score for our 1190 kg pumpkin, it's gonna be equal to 1190 minus 5.2, OK, divided by 1.8. And that would be equal to 658.22. That's our Z square. Next, for a second Z score for the smaller weight, it's going to be 0.45 minus 5.2 divided by 1.8. That's -4.75 divided by 1.8, which equals -2.64, which means its absolute value then is going to be 2.64. Likewise, the absolute value of our first Z score is 658.22. Now what does this tell us? Well, here, notice that the Z score of the larger pumpkin is much or the absolute value of that Z score is much higher in absolute value than that of the smaller pumpkin. Thus, this tells us that it is the more extreme value. Therefore, the largest pumpkin has the more extreme weight. A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Key Concepts

Z-Score

Mean and Standard Deviation

Comparative Analysis

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