The following problems are all for populations You took a test in statistics and
ID: 3305656 • Letter: T
Question
The following problems are all for populations You took a test in statistics and scored 71/100. The mean is 68 and the standard deviation is 5 A: Calculate your Z-score-the formula is (xIscore you are wondering about)-M(mean of the population))/N or (X-MN 5 B: On the z-table in your book (or feel free to google it),find out what percentage of scores you are above. To do this, you will check the z score you got and see what % it corresponds to (should be 4 digit decimal) and multiply by 100 (to get % out of 100) C: How would your percentage change if the standard deviation were larger, for instance 8? calculate your new z score and percentage belo 2: Z decimal from table Percentage D: If there were 46 kids in your class, how many of them scored ABOVE you? You now have to transform the data again, what is r%(this should be what you got for the % in C) of 46 kids? Multiply the total N by the original Z decimal· kids that scored at or below. Now to find out how many scored above, you calculate the remainder, or 46-(# that scored at or below) kids scored above you. Not badl E: Seeing the difference in the two percentages in A and C, why is standard deviation important? Problem set 2 A: You tried to run a SK for the first time (go youl) and ran it in 25 minutes and 15 seconds. The average time for SK runs is 12 minutes and 3 seconds. The standard deviation is 4.25 minutes. What percentile are you in? Hint: you need to transform your time and the average time so there are no seconds left (e.g. 25.,00 minutes and 12.D0 minutes) 25-12 42S .0 (1) 3.o6 (1) B: If 1776 people ran the SK with you, how many did you run the 5K faster than? C: If you ran it in 19.5 minutes the second time, what percentage of CHANGE is there? *Hint: subtract your original z percentile from your new z percentile. 145-12: 1.76(z) 4.26Explanation / Answer
b):
From z table z-score 0.6 has 0.7257 area to its left.
So,
Percentage of z scores you are above is 0.7257 *100 = 72.57%.
c)
The new z-score is
z = ( 71-68) /8 = 0.375
Now from z table, z-score 0.375 is 0.6462. It is average of area left to z-scores 0.37 and 0.38.
So requried percentage is 0.6462 * 100 = 64.62%
d)
Kids that are below you: 0.6462 *46 = 29.7252
That is approximately 30 kids are below you. So kids that are above you: 46 - 30 = 16.
e)
As the standard deviation increases, percentage of kids below or at your score decreases.
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