Glad To See You Again Lv Team!. These Past Few Weeks We

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Glad to see you again LV Team!

These past few weeks we have covered the central tendency, variability, correlation and now we will look at something that has a correlation with standard deviation and mean. I hope you still remember the bell shape of the standard deviation graph! That is ok, if you do not. I will briefly do my best to summarize it. The Standard Deviation (SD) is the average distance from the mean. In a normal distribution, the standard deviation is the standard that is 34 % of the cases to the right that would be one positive standard deviation and 34% to the left and that would be one negative SD. Majority of the data will be between -3 and +3 standard deviation from the mean; which is applicable to all normal
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For example, chemistry and physics grade are completely different; however, if one has the SD, mean then one could find out the z-score to compare the location. Mary got a score of 70, SD= 10 and mean of 60 on a chemistry exam. She also got a score of 80, SD= 5, mean= 75 for physics.
Z-score for chemistry= (70-60)/1= 1
Z-score for physics= (80-75)/10= 0.5
We can say that Mary’s score for chemistry was 1 SD above the class mean and physics was 0.5 above the class mean.
Let’s do some more practices!
***The following four cases are based on a normal distribution of scores with Mean = 75 and the SD = 6.38.
¥ What is the probability of a score falling between a raw score of 70 and 80?
We are in Olive oil business and we would like to know the probability of selling 70 to 80 bottles? The average mean is 75 and the SD is 6.38 Z= (70-75)/6.38= -0.78 Z= (80-75)/6.38= 0.78
Once we get the z-score, we want to convert it to probability values. We know at 1value it is 34% but we have only 0.78. We will use the appendix D that is on the screen, find 0.78 in section A (z value) and run your finger to section B (area between mean and Z). The results are 0.2823 convert in %; which is 28.23%. One thing, there is no negative z values in the appendix because it symmetrical. So to the right of the mean it is 28.23% and to the left 28.23%; with a total % of 56.46%.
The probability of selling 70 to 80 bottles would be 56.46%.
What is the probability of a score falling above a

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