The commute times (i.e., amount of time it takes to get from home to work) for...

  

Transcribed Image Text:

The commute times (i.e., amount of time it takes to get from home to work) for office employees are Normally distributed, with a mean of 35 minutes and a standard deviation of 4 minutes. Please use this information to answer Questions 1 through 12. Hint: Remember that a very useful first step in these types of problems involves drawing the distribution and marking it out three standard deviations on either side of the mean. To help you get started, we've shared a Normal curve with you below. Please mark it accordingly, if you wish, as you work through the first part of this assignment. 1. The Empirical Rule (or the 68-95-99.7 Rule) tells us that approximately 95% of the commute times are between minutes and minutes. 2. Angela's commute time is 29.4 minutes. This means that Angela is at what percentile? 3. Dwight's commute time is 42.2 minutes. What percentage of office employees have smaller (or shorter) commute times than Dwight? 4. Toby has a commute time of 45 minutes. This means that Toby is at what percentile? 5. Return to Question 4. What percentage of office employees have commute times that are larger (or longer) than Toby's commute time? 6. Stanley has a commute time of 36.3 minutes. What percentage of office employees have commute times that are larger (or longer) than Stanley's commute time? 7. What percentage of office employees have commute times between 36.3 minutes and 45 minutes? 8. If Kelly is at approximately the 18th percentile in this distribution, this means that Kelly has a commute time of approximately minutes. 9. If Oscar is at the 93rd percentile in this distribution, this means that Oscar has a commute time of approximately minutes. 10. Meredith's commute time is at the first quartile (or Q₁). This means that Meredith's commute time is approximately minutes. 11. Jim's commute time is at the third quartile (or Q3). This means that Jim's commute time is approximately minutes. 3 12. Think about where the median would be in the distribution of commute times. An office employee who has a commute time that is equal to the median would have a standard score equal to what value? Part 2: What went wrong? Once again, we wondered what would happen if we asked ChatGPT to try to help us with some Normal distribution problems. We were disappointed by the results. Read carefully through the ChatGPT, output below in order to answer Question 13. Note the output begins with the prompt we gave ChatGPT, and it's followed by ChatGPT's response. The pulse rates (or number of heart beats per minute) for a large population of adults are Normally distributed, with a mean of 70.1 beats per minute and a standard deviation of 11.4 beats per minute. When Sam's pulse rate is converted to a z-score, it is found that z = 0. What does this mean? A. Sam's pulse rate is equal to the median pulse rate. B. Sam's pulse rate is below the 50th percentile. C. Sam's pulse rate is below average. D. Sam has no pulse. E. None of the above answer options are correct. ChatGPT When Sam's pulse rate is converted to a z-score, and it is found that z = 0, this means: B. Sam's pulse rate is below the 50th percentile. A z-score of 0 indicates that Sam's pulse rate is at the mean of the population (in this case, 70.1 beats per minute), which corresponds to the 50th percentile in a normal distribution. It does not necessarily mean that Sam's pulse rate is below average or equal to the median (which would also be the same as the mean in a normal distribution). It simply means that Sam's pulse rate is at the population's average or at the 50th percentile. 13. Something is wrong with the answer (or response) given by ChatGPT. What do you think is wrong? Please explain. The commute times (i.e., amount of time it takes to get from home to work) for office employees are Normally distributed, with a mean of 35 minutes and a standard deviation of 4 minutes. Please use this information to answer Questions 1 through 12. Hint: Remember that a very useful first step in these types of problems involves drawing the distribution and marking it out three standard deviations on either side of the mean. To help you get started, we've shared a Normal curve with you below. Please mark it accordingly, if you wish, as you work through the first part of this assignment. 1. The Empirical Rule (or the 68-95-99.7 Rule) tells us that approximately 95% of the commute times are between minutes and minutes. 2. Angela's commute time is 29.4 minutes. This means that Angela is at what percentile? 3. Dwight's commute time is 42.2 minutes. What percentage of office employees have smaller (or shorter) commute times than Dwight? 4. Toby has a commute time of 45 minutes. This means that Toby is at what percentile? 5. Return to Question 4. What percentage of office employees have commute times that are larger (or longer) than Toby's commute time? 6. Stanley has a commute time of 36.3 minutes. What percentage of office employees have commute times that are larger (or longer) than Stanley's commute time? 7. What percentage of office employees have commute times between 36.3 minutes and 45 minutes? 8. If Kelly is at approximately the 18th percentile in this distribution, this means that Kelly has a commute time of approximately minutes. 9. If Oscar is at the 93rd percentile in this distribution, this means that Oscar has a commute time of approximately minutes. 10. Meredith's commute time is at the first quartile (or Q₁). This means that Meredith's commute time is approximately minutes. 11. Jim's commute time is at the third quartile (or Q3). This means that Jim's commute time is approximately minutes. 3 12. Think about where the median would be in the distribution of commute times. An office employee who has a commute time that is equal to the median would have a standard score equal to what value? Part 2: What went wrong? Once again, we wondered what would happen if we asked ChatGPT to try to help us with some Normal distribution problems. We were disappointed by the results. Read carefully through the ChatGPT, output below in order to answer Question 13. Note the output begins with the prompt we gave ChatGPT, and it's followed by ChatGPT's response. The pulse rates (or number of heart beats per minute) for a large population of adults are Normally distributed, with a mean of 70.1 beats per minute and a standard deviation of 11.4 beats per minute. When Sam's pulse rate is converted to a z-score, it is found that z = 0. What does this mean? A. Sam's pulse rate is equal to the median pulse rate. B. Sam's pulse rate is below the 50th percentile. C. Sam's pulse rate is below average. D. Sam has no pulse. E. None of the above answer options are correct. ChatGPT When Sam's pulse rate is converted to a z-score, and it is found that z = 0, this means: B. Sam's pulse rate is below the 50th percentile. A z-score of 0 indicates that Sam's pulse rate is at the mean of the population (in this case, 70.1 beats per minute), which corresponds to the 50th percentile in a normal distribution. It does not necessarily mean that Sam's pulse rate is below average or equal to the median (which would also be the same as the mean in a normal distribution). It simply means that Sam's pulse rate is at the population's average or at the 50th percentile. 13. Something is wrong with the answer (or response) given by ChatGPT. What do you think is wrong? Please explain.