Download A z-score gives us an indication of how unusual a value is because

Z-Score Day 2
Tuesday, October 22nd
A z-score gives us an indication of how unusual a value is because it tells us how ____________
_______________________.
 If the data falls _________________, it is not very far at all and the z-score is ____.
 A z-score of 1 tells us that the data value is 1 standard deviation above the mean.
 A z-score of -1 tells us that the data value is 1 standard deviation below the mean.
So, how far from 0 does z-score have to be to be interesting or unusual?
No matter what the shape of the data, “normal” or not, a z-score of 3 or -3 is rare, and a
z-score of ________________________________________________________.
Application: The SAT Reasoning Test has three parts: Writing, Math, and Critical Reading
(Verbal). Each part has a distribution that is roughly symmetric and is designed
to have an overall mean of about 500 and a standard deviation of 100 for all test takers.
In any one year, the mean and standard deviation may differ from these target values
by a small amount, but they are a good overall approximation.
Suppose you earn a 600 on one part of your SAT. Where do you stand among all the
students who took the test?
Create and label a normal curve for this data. Use the 68-95-99.7 Rule to describe the data.
Application 2: Suppose your Statistics professor reports test grades as z-scores, and you got a score
of 2.20 on an exam. Write a sentence explaining what that means.
Application 3: A runner receives his mile time as a z-score, and gets a -1.3. Write a sentence
explaining what that means. Explain how the negative sign helps you describe
whether the time is above or below the mean in this case. How does this differ from the
previous problem?
Application 4: The mean score on a Stats exam was 75 points with a standard deviation of 5
points, and Gregory’s z-score was a -2. How many points did he score?
Application 5: People with z-scores above 2.5 on an IQ test are sometimes classified as
geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points,
what IQ score do you need to be considered a genius?