RESPONDING TO DISCUSSION 300 WORDS EACH RESPOND TO THE ATTACHMENT RESPOND IN 300 WORDS:
The Z-score allows one to estimate the probability of a score. This could be needing to know how low or how high to score on an exam to pass or fail. Knowing the mean and the standard deviation will allow one to convert to a z table to know the percentage of a score. Just knowing the mean and score only accommodates one score and average related to all collected data. Knowing your score on an exam and the mean of all other exams will not answer the score desired or needed to pass. If a student was failing and had two more tests coming up, the z-score could be utilized to determine grade needed to pass.
A score at the mean is equal to a z score of 0. A score 1 SD above the mean would be equal to a z score of +1.0. A score 1 below the mean would equal to a z score of -1.0″ (Week3 Lecture 1).
Example: Using information below on charts provided
Rounding to a mean of 85, and SD of 6. The mean of 85 is the middle or 50% out of 100% on a normal distribution bell curve. To get the top 25% you would utilize the mean and SD to convert to a z score. A z score consists of a table with the given criteria. To accommodate the top 25%, you need to get the percentage of at least 75%. On a Z table .68 is 75.17, which meets the 75% needed. Now one would take that .68 multiply by SD and add the mean. .68×6+85=89.08. Looking at the information below Crystal and Skylar are in the top 25%.
RESPOND IN 300N WORDS:
One of the primary purposes of a z-score is to describing the exact location of a score within a distribution. The z-score accomplishes this goal by transforming each X value into a signed number (+or-) the sign tells whether the score is located above (+) or below (-) the mean and the number tells the distance between the score and the mean in terms of the number of standard deviations.
When describing how an individual performed on an exam you need the z-score to get more information. If you just have the mean and the value of the score, you still would need the standard deviation to have all the information to get the correct z-score.
Students Test Scores Z-Scores
S1 175 -0.360624459
S2 206 1.831406566
S3 150 -2.128391415
S4 165 -1.067731241
S5 180 -0.007071068
S6 210 2.114249279
S7 200 1.407142497
S8 190 0.700035715
S9 170 -0.71417785
S10 155 -1.774838024
M of Scores 180.1
SD of Scores 14.14213562
When you have the z-score you are getting the standardized score that shows a little more about the average out of the ten students.