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4. How do you interpret a z - score? 5. How to calculate a raw score when a z- score is known?

4. How do you interpret a z - score? 5. How to calculate a raw score when a z- score is known?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Az-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean. It is also known as a standard score, because it allows comparison scores on different kinds variables by standardizing the distribution. To further understand the application of z - score for any normally distributed data, answer the following problems. 1. Rodrigo earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Rodrigo? (Assume that test scores are normally distributed.) If there were 100,000 students who took the test, how many would be expected to have a higher score than Rodrigo? 2. The following letter appeared in the popular "Dear Abby" newspaper advice column in the 1970s: Dear Abby: You wrote in your column that a woman is pregnant for 266 days. Who said so? I carried my baby for ten months and five days, and there is no doubt about it because I know the exact date my baby was conceived. My husband is in the Navy and it couldn't have possibly been conceived any other time because I saw him only once for an hour, and I didn't see him again until the day before the baby was born. 203 I don't drink or run around, and there is no way this baby isn't his, so please print a retraction about the 266-day carrying time because otherwise I am in a lot of trouble. San Diego Reader The advice column was founded in 1956 by Pauline Phillips under the pen name "Abigail Van Buren" and caried on up to today by her daughter, Jeanne Phillips, who now owns the legal rights to the pseudonym. Suppose that according to pediatricians, pregnancy durations, let's call them X, tend to be normally distributed with m= 266 days and s = 16 days. Perform a probability calculation that addresses San Diego Reader's credibility, presuming she was pregnant for 308 days. What would you conclude and why? 3. Why are z- scores important? 4. How do you interpret a z - score? 5. How to calculate a raw score when a z - score is known?
Transcribed Image Text:Az-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean. It is also known as a standard score, because it allows comparison scores on different kinds variables by standardizing the distribution. To further understand the application of z - score for any normally distributed data, answer the following problems. 1. Rodrigo earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What proportion of students had a higher score than Rodrigo? (Assume that test scores are normally distributed.) If there were 100,000 students who took the test, how many would be expected to have a higher score than Rodrigo? 2. The following letter appeared in the popular "Dear Abby" newspaper advice column in the 1970s: Dear Abby: You wrote in your column that a woman is pregnant for 266 days. Who said so? I carried my baby for ten months and five days, and there is no doubt about it because I know the exact date my baby was conceived. My husband is in the Navy and it couldn't have possibly been conceived any other time because I saw him only once for an hour, and I didn't see him again until the day before the baby was born. 203 I don't drink or run around, and there is no way this baby isn't his, so please print a retraction about the 266-day carrying time because otherwise I am in a lot of trouble. San Diego Reader The advice column was founded in 1956 by Pauline Phillips under the pen name "Abigail Van Buren" and caried on up to today by her daughter, Jeanne Phillips, who now owns the legal rights to the pseudonym. Suppose that according to pediatricians, pregnancy durations, let's call them X, tend to be normally distributed with m= 266 days and s = 16 days. Perform a probability calculation that addresses San Diego Reader's credibility, presuming she was pregnant for 308 days. What would you conclude and why? 3. Why are z- scores important? 4. How do you interpret a z - score? 5. How to calculate a raw score when a z - score is known?
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