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A professor gives a test worth 100 points. The mean is 95, and the standard deviation is 4. Is it possible to apply a normal distribution to this situation? Why or why not? Choose the correct answer below. O A. Yes, because in this situation the distribution is skewed to the left. B. No, because the standard deviation must be greater than 4. O C. Yes, because in this situation the distribution is symmetric about the mean. D. No, because in this situation the distribution is skewed to the left.

A professor gives a test worth 100 points. The mean is 95, and the standard deviation is 4. Is it possible to apply a normal distribution to this situation? Why or why not? Choose the correct answer below. O A. Yes, because in this situation the distribution is skewed to the left. B. No, because the standard deviation must be greater than 4. O C. Yes, because in this situation the distribution is symmetric about the mean. D. No, because in this situation the distribution is skewed to the left.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Understanding Normal Distribution in Test Scores A professor gives a test worth 100 points. The mean is 95, and the standard deviation is 4. Is it possible to apply a normal distribution to this situation? Why or why not? --- #### Choose the correct answer below: - **A. Yes, because in this situation the distribution is skewed to the left.** - **B. No, because the standard deviation must be greater than 4.** - **C. Yes, because in this situation the distribution is symmetric about the mean.** - **D. No, because in this situation the distribution is skewed to the left.** (Selected) --- ### Analysis: In order to determine whether it is appropriate to apply a normal distribution to this situation, we need to consider the properties of normal distribution: 1. **Symmetry:** Normal distribution is symmetric about the mean. 2. **Empirical Rule:** Approximately 68% of the data falls within one standard deviation of the mean, approximately 95% within two standard deviations, and approximately 99.7% within three standard deviations. 3. **Skewness:** Normal distribution is not skewed; it has a skewness of 0. #### Given Data: - **Mean (μ):** 95 - **Standard Deviation (σ):** 4 - **Test Worth:** 100 points The skewness and symmetry of the data related to applying a normal distribution needs to be considered. If the distribution of the test scores is symmetric about the mean and not skewed, a normal distribution can be applied. Given the correctness of the selected option, this scenario considers skewness. ### Conclusion: Option **D** suggests that the distribution is skewed to the left and hence, a normal distribution is not appropriate. Therefore, based on the provided answer, the correct interpretation involves recognizing the skewness in the given situation and determining that applying a normal distribution would not be accurate.
Transcribed Image Text:### Understanding Normal Distribution in Test Scores A professor gives a test worth 100 points. The mean is 95, and the standard deviation is 4. Is it possible to apply a normal distribution to this situation? Why or why not? --- #### Choose the correct answer below: - **A. Yes, because in this situation the distribution is skewed to the left.** - **B. No, because the standard deviation must be greater than 4.** - **C. Yes, because in this situation the distribution is symmetric about the mean.** - **D. No, because in this situation the distribution is skewed to the left.** (Selected) --- ### Analysis: In order to determine whether it is appropriate to apply a normal distribution to this situation, we need to consider the properties of normal distribution: 1. **Symmetry:** Normal distribution is symmetric about the mean. 2. **Empirical Rule:** Approximately 68% of the data falls within one standard deviation of the mean, approximately 95% within two standard deviations, and approximately 99.7% within three standard deviations. 3. **Skewness:** Normal distribution is not skewed; it has a skewness of 0. #### Given Data: - **Mean (μ):** 95 - **Standard Deviation (σ):** 4 - **Test Worth:** 100 points The skewness and symmetry of the data related to applying a normal distribution needs to be considered. If the distribution of the test scores is symmetric about the mean and not skewed, a normal distribution can be applied. Given the correctness of the selected option, this scenario considers skewness. ### Conclusion: Option **D** suggests that the distribution is skewed to the left and hence, a normal distribution is not appropriate. Therefore, based on the provided answer, the correct interpretation involves recognizing the skewness in the given situation and determining that applying a normal distribution would not be accurate.
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