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Normal distributions are a family of distributions with a symmetrical bell shape:-The area under each of the curves above is the same and most of the values occur in the middle of the curve. The mean and standard deviation of a normal distribution control how tall and wide it is. Download a free trial here. McAfee won't let me download ANYTHING! I am facing issue of not letting me download anything. Suddenly McAfee is not allowing me to download anything and says 'virus scan failed'. This is happening even after i have completely uninstalled this annoying software from my laptop.

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If you upgraded straight from Windows 7 (as I did), you might never have used this store before. As with any app store, it’s filled with junk, but these are a few free apps you should consider downloading in order to make your Windows 10 experience better.

Adobe Photoshop Express

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If you need a professional photo editing suite, the full Adobe Photoshop is worth every penny, but if something more limited will suffice, you might want to check out Photoshop Express. Plus, if you decide you want more themes or features, you can always pay for them via in-app purchases.

Flixster

Want to see the Tomatometer for a recent movie? Looking to get showtimes for a movie releasing this weekend? Flixster is an app you should have on your desktop. It’s a great all-in-one solution for any regular moviegoer.

StumbleUpon

The StumbleUpon fad came and went fairly quickly a few years ago, but it’s still a fun app to peruse while you’re bored at the office or can’t get to sleep at night.

TuneIn Radio

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VLC

The media player situation on Windows 10 is a bit of a mess, especially when it comes to the ridiculous $15 app Microsoft is attempting to charge customers for in order to watch DVDs. VLC is a far better solution, and it’s free to download from the Windows Store.

Menu location: Analysis_Distributions_Normal.

The standard normal distribution is the most important continuous probability distribution. It was first described by De Moivre in 1733 and subsequently by the German mathematician C. F. Gauss (1777 - 1885). StatsDirect gives you tail areas and percentage points for this distribution (Hill, 1973; Odeh and Evans, 1974; Wichura, 1988; Johnson and Kotz, 1970).

Normal distributions are a family of distributions with a symmetrical bell shape:-

The area under each of the curves above is the same and most of the values occur in the middle of the curve. The mean and standard deviation of a normal distribution control how tall and wide it is.

The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Any point (x) from a normal distribution can be converted to the standard normal distribution (z) with the formula z = (x-mean) / standard deviation. z for any particular x value shows how many standard deviations x is away from the mean for all x values. For example, if 1.4m is the height of a school pupil where the mean for pupils of his age/sex/ethnicity is 1.2m with a standard deviation of 0.4 then z = (1.4-1.2) / 0.4 = 0.5, i.e. the pupil is half a standard deviation from the mean (value at centre of curve).

The diagram above shows the bell shaped curve of a normal (Gaussian) distribution superimposed on a histogram of a sample from a normal distribution. Many populations display normal or near normal distributions. There are also many mathematical relationships between normal and other distributions. Most statistical methods make 'normal approximations' when samples are sufficiently large.

Central Limit Theorem

In order to understand why 'normal approximations' can be made, consider the central limit theorem. The central limit theorem may be explained as follows: If you take a sample from a population with some arbitrary distribution, the sample mean will, in the limit, tend to be normally distributed with the same mean as the population and with a variance equal to the population variance divided by the sample size. A histogram plot of the means of many samples drawn from one population will therefore form a normal (bell shaped) curve regardless of the distribution of the population values.

Technical Validation

The tail area of the normal distribution is evaluated to 15 decimal places of accuracy using the complement of the error function (Abramowitz and Stegun, 1964; Johnson and Kotz, 1970). The quantiles of the normal distribution are calculated to 15 decimal places using a method based upon AS 241 (Wichura, 1988).

z0.001 = -3.09023230616781

Lower tail P(z= -3.09023230616781) = 0.001

z0.25 = -0.674489750196082

Lower tail P(z= 0.674489750196082) = 0.25

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z1E-20 = -9.26234008979841

Lower tail P(z= -9.26234008979841) = 9.99999999999962E-21

The first two StatsDirect results above agree to 15 decimal places with the reference data of Wichura (1988). The extreme value (lower tail P of 1E-20) evaluates correctly to 14 decimal places.

Function Definition

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Distribution function, Φ(z), of a standard normal variable z:

StatsDirect calculates Φ(z) from the complement of the error function (errc):