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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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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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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