z Scores If your score on your next statistics test is convert...

Question

z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?

Accepted Answer

Welcome back, everyone. In this problem, a student's math test is converted into a Z square. Which of the following Z scores would the student prefer? -1.5, 0 0.5, 0, 1.5, or 2.5? A says it would be -1.5, B negative 0.5, C 0, D 1.5, and E 2.5. Now what do we know about the Z square that can help us to figure out which one the student would prefer? Well, recall that a Z2 tells us how many standard deviations a value is from the mean, and we calculate it by subtracting the mean from a value and dividing by the standard deviation. In this case, the value would be the individual square, and we're talking about the mean and standard deviation of the data set. If we get a negative Z score, that means the score is below the mean. A positive Z score means the score is above the mean, and a Z score of 0 means the score is exactly at the mean. So given our Z scores, which one would our student like? Well, we know that our student wants to pass, OK? So, if we interpret each of these Z scores, a Z score of -1.5 means that our score is 1.5 standard deviations below the mean, OK? So, -1.5. Means 1.5 standard deviations below the mean, and that's not what our student would want. A Z score of negative 0.5 then means 0.5 standard deviations below the mean, OK? If we think about it, 0, then it's not like 0, but rather 0. Would mean that the standard deviation is exactly at the mean, OK. Or in other words, our score rather, our score means our score is at the mean. 1.5 would mean it's 1.5 standard deviations above the mean. That's a good score, and 2.5 means it's, it's 2.5 standard deviations above the mean. That's an excellent score. So a higher Z score means a better performance. A negative Z score would be undesirable, and a positive Z score would indicate above average performance. So I think a Z score of 2.5 would be best as it represents the highest test score. Therefore, E is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

��app