### Z-Score and Normal Distribution Calculation**Question:**A normal distribution has a data point 28.2 with a z-score of 1.4. If the standard deviation is 3.8, what is the mean?**Options:**- 22.88- 28.2- 33.52- 11.75**Detailed Explanation:**Let’s use the z-score formula to calculate the mean, where:\[ \text{z-score} = \frac{(x - \mu)}{\sigma} \]Given:- Data point $ x = 28.2 $- Z-score $ z = 1.4 $- Standard deviation $ \sigma = 3.8 $We need to find the mean $ \mu $. Rearrange the formula to solve for $ \mu $:\[ \mu = x - z \cdot \sigma \]Substitute the given values into the equation:\[ \mu = 28.2 - 1.4 \cdot 3.8 \]\[ \mu = 28.2 - 5.32 \]\[ \mu = 22.88 \]Therefore, the mean of the distribution is **22.88**.**Correct Answer: 22.88**

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A normal distribution has a data point 28.2 with a z-score of 1.4. If the standard deviation is 3.8, what is the mean? 22.88 28.2 33.52 11.75

Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

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