Question
Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true? Neither the means nor the standard deviations of Dwayne's and Alisha's graphs must be the same. The means of Dwayne's and Alisha's graphs must be the same but not the standard deviations. The standard deviations of Dwayne's and Alisha's graphs must be the same but not the means. Both the means and the standard deviations of Dwayne's and Alisha's graphs must be the same. Bres
Ask by Reed Cruz. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Both Dwayne and Alisha must have the same mean and standard deviation for their standard normal curves.
Solution
A standard normal curve by definition has a mean of 0 and a standard deviation of 1. Therefore, if both Dwayne and Alisha correctly graphed a standard normal curve, they must both have used a mean of 0 and a standard deviation of 1.
Thus, the correct answer is: Both the means and the standard deviations of Dwayne's and Alisha's graphs must be the same.
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Simplify this solution Bonus Knowledge
In the realm of standard normal curves, both Dwayne and Alisha's graphs represent the same fundamental distribution. This means that their means must be identical, specifically at 0, and their standard deviations must also match, set at 1. Thus, if both graphs are standard normal curves, their characteristics are uniform. If you're diving deeper into the world of statistics, exploring concepts like the Z-score, which standardizes scores onto this curve, can be enlightening. Understanding how to transform different distributions into a standard normal form enhances your analytical skills and reveals the beauty of statistical relationships!
