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If a distribution is normal but not standard, we can convert a value to the Standard normal distribution table by first by finding how many standard deviations away the number is from the mean.
The z-score
The number of standard deviations from the mean is called the z-score and can be found by the formula
x - m z = s
Example
Find the z-score corresponding to a raw score of 132 from a normal distribution with mean 100 and standard deviation 15.
Solution
We compute
132 - 100 z = = 2.133 15
Example
A z-score of 1.7 was found from an observation coming from a normal distribution with mean 14 and standard deviation 3. Find the raw score.
Solution
We have
x - 14 1.7 = 3
To solve this we just multiply both sides by the denominator 3,
(1.7)(3) = x - 14
5.1 = x - 14
x = 19.1
The z-score and Area
Often we want to find the probability that a z-score will be less than a given value, greater than a given value, or in between two values. To accomplish this, we use the table from the textbook and a few properties about the normal distribution.
Example
Find
P(z < 2.37)
Solution
We use the table. Notice the picture on the table has shaded region corresponding to the area to the left (below) a z-score. This is exactly what we want. Below are a few lines of the table.
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
2.2
.9861
.9864
.9868
.9871
.9875
.9878
.9881
.9884
.9887
.9890
2.3
.9893
.9896
.9898
.9901
.9904
.9906
.9909
.9911
.9913
.9916
2.4
.9918
.9920
.9922
.9925
.9927
.9929
.9931
.9932
.9934
.9936
The columns corresponds to the ones and tenths digits of the z-score and the rows correspond to the hundredths digits. For our problem we want the row 2.3 (from 2.37) and the row .07 (from 2.37). The number in the table that matches this is.9911.
Hence
P(z < 2.37) = .9911
Example
Find
P(z > 1.82)
Solution
In this case, we want the area to the right of 1.82. This is not what is given in the table. Grand total 5 2 6 cyl. We can use the identity
Once again, the table does not exactly handle this type of area. However, the area between -1.18 and 2.1 is equal to the area to the left of 2.1 minus the area to the left of -1.18. That is
P(-1.18 < z < 2.1) = P(z < 2.1) - P(z < -1.18)
To find P(z < 2.1) we rewrite it as P(z < 2.10) and use the table to get
P(z < 2.10) = .9821.
The table also tells us that
P(z < -1.18) = .1190
Now subtract to get
P(-1.18 < z < 2.1) = .9821 - .1190 = .8631
e-mail Questions and Suggestions
TotalFinder is an awesome Finder plugin for Mac that adds tabs, hotkeys, and other tweaks to your Mac OS X Finder in 10.6 Snow Leopard or 10.7 Lion.
The Finder application that is provided as default is well-integrated with the TotalFinder that places several options for customization in the panel that has been added to the ones provided as default in the window of the Finder Preferences. By this way the Finder of yours is not changed or altered.
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The developer of this application was Antonin Hildebrand and he pointed out at least a minimum of two ways for successfully uninstalling the application through the various options available in the status bar of the TotalFinder or by using the uninstaller that is available in the archive of the application.
You can keep the application of TotalFinder installed even if you do not use them but you are only required to remove it from the items of the login startup list and you can easily launch it at any time when you feel the need to create it.
The Visor feature contains a pretty important part of this application and the icon on the status menu is displayed in white as well as black on disabling this feature and colors are shown in case if it is in the active state.
TotalFinder always tends to work on the default features of the Finder and it is really a very important thing that you must understand.
The toolbar is always displayed on the very top of the Finder window, while the sidebar is displayed on the left-hand side and the contents of the folder in the right-hand side, at the bottom is provided the information bar while the button present in the upper right corner on the top is used for toggling the sidebar.
Totalfinder 1 7 14 Commentary
Features of TotalFinder
Simple Tabbed Browsing : Tabs can be added on the top of the Finder. The tabs that are visible in the Google Chrome is also visible here.
Dual Mode : A dual mode displays the window of two Finders in a side-by-side mode.
Folders of Top : In the very beginning of the list view folders are provided.
Show System Files : It show you all files of your Disk.
Visor : Convenient system-wide Finder always one key-press away.
Cut and Paste Functionality : The various Keyboard shortcuts are used to transfer the files all around in a faster and easier way. Faster and better than drag & drop.
