Standard Normal Probability Distributions With Microsoft Excel

Traditionally, to find the standard normal probability distribution, you must convert the normal random variable x to the standard normal distribution using the z-value formula, and then find the area under the standard normal distribution function below z. The normal probability distribution functions described earlier in this chapter shortens this process. The Standard Normal Probability Distribution has a mean of 0 and a standard deviation of 1.

NORMSDIST

If you already have a z value, or if you’ve used the z-value formula STANDARDIZE described below to find a z-value, you can use the NORMSDIST function to find the probability that a random variable x is below z standard deviations from the mean. The NORMSDIST function uses the following syntax:

=NORMSDIST (z-value)

For example, if you create furniture that needs to fit people of various heights and know that the average American adult is 5’8″ tall, and the heights are normally distributed around this mean with a standard deviation of 4″, you can find the probability that one of your customers is less than 6’2″.

To use this function, you must first convert the data to the standard normal distribution as described below under “STANDARDIZE.” Doing so returns a z value of 1.5, meaning that 6’2″ is 1.5 standard deviations above the mean. When you enter 1.5 as the z-value parameter of the NORMSDIST function, the function returns the value 0.9331.

If you want to find the probability that a person is greater than 6’2″ tall, you just subtract this value from 1. If you want to find the probability that a person is between 5’4″ and 6′, you must make a few calculations. The probability that a person is less than 6′ tall is 0.8413. This means that the probability that a person is between the mean (5’8″) and 6′ is .3413 (because the probability that a person is less than 5’8″ is 0.5). Likewise, the probability that a person is between 5’4″ and 5’8″ is .34134474. Add these together to get 0.6826.

NORMSINV

If instead of having a value and needing to find the probability that a random variable falls below it, you know the probability for the range into which a random variable must fall and need to find the value defining this range, you can use the NORMSINV function.

To use the NORMSINV function, just enter the probability (between 0 and 1, of course) and the function returns the z-value below which the probability area you entered falls. If you choose a probability less than 0.5, the function returns a negative z-value. If you enter a probability greater than 0.5, the function returns a positive z-value. The NORMSINV function uses the following syntax:

=NORMSINV (probability)

STANDARDIZE

Traditionally, to answer probability questions about a normal distribution, you first convert the distribution to the standard normal distribution. The standard normal distribution has a mean of zero and a standard deviation of 1. To convert to the standard normal distribution, you find a z value using the STANDARDIZE function in Excel. The STANDARDIZE function uses the following syntax:

=STANDARDIZE(x, mean, standard deviation)

For example, if you have a product that costs an average of $6,000 to produce and a standard deviation of $800, what percentage of the items should you expect to cost more than $6,600?

To find out, enter the function as follows:

=STANDARDIZE (6600,6000,800)

The function returns the value .75. You can then use the NORMSDIST function to find the probability or area under the curve between 0 and .75.

The z-value tells you how far (in terms of the number of standard deviations) an individual observation is from the mean. It therefore also allows you to determine whether an observation

is an outlier (unusually large or small) and therefore suspect. Z-values of less than –3 or greater than +3 are generally treated as outliers and call for closer inspection.

Kiat Esemka,the cars from Indonesia

This student-made cars Kiat Esemka Vocational School (SMK), which became the pride of Solo Mayor Joko Widodo. I was so proud, two cars vocational students and vocational Citizens Surakarta Indonesia is used as an official car by Joko Widodo.

This car-type SUV (Sport Utility Vehicle), painted black. With a capacity of 1,500 cc, the car with the engine adopted from the Timor car can produce 105 horsepower power with engine speed 5,500 rpm.

In terms of exterior, this car looks fierce and elegant. That’s thanks to a touch of stylish models head lamp. The impression was also seen on the sporty grille and fog lamp in the bumper. While in the interior, the car that has a capacity of seven passengers, equipped with power windows, dual zone air conditioning, power steering, central lock, audio system with CD, and do not miss parking sensors.

Top 15 List of MLM Companies in Singapore

If you have been looking for a list of MLM companies in Singapore we have the top fifteen here for you to look over. Starting a new home based business can sometimes be stressful, trying to figure out which one of the thousands of MLM companies are worth investing your hard earned money into hoping to make a profit. While taking a look at the ones below, think about if any information we provide is things you are looking for in a company.

Eleven out of the top fifteen are internationally known, but the other four (Venture Era Local, LongFar China, WBG Local, Best World Local) were started in Singapore. This list of MLM companies also includes common names such as Amway, NuSkin, and Melaleuca which cover three of the top 5 overall. Since you can do the research on all of these companies we thought we could at least get you started with a couple of them finding out what exactly they do for the MLM world and cost to join, etc..

You will find NeWays International at #3 on the list of MLM companies in Singapore, selling nutritional products as well as personal care products. At first look this sounds like a thousand other health companies, but NeWays offers not only natural ingredients that, but longevity starting out in 1992. Positioned in twenty-nine countries the company has over five hundred thousand (500,000) distributors world wide, providing their own manufacturing plants in Utah.

As of February 2008 Neways offers a free enrollment with the opportunity to receive a free product that you can try for yourself or sell and keep the entire product. There are six to choose from ranging from $6.90 in price to $35.90, and also you will get a starter kit when you sign up. This will give you all the tools you will need to work towards becoming successful with NeWays International. Its a great starting contribution from this list of MLM companies.

Rounding out the top 5 of this list of MLM companies is Usana International which not only is a health and wellness company as well, but also has its main headquarters in Utah. Usana is the same company that in 2006 signed an agreement with the WTA (Women’s Tennis Association) where the players would be distributed Usana products due to allegations in recent years of illegal substances in professional sports.

Usana International began in 1992 and now covers fourteen different countries recording almost $450 million in sales per year. Looking at the top 15 list of MLM companies we came across an interesting fact to Usana’s products, its a skin care product called; Sense. We found that the shelf life for this product is two years leaving Sense as the only company in the world with a patent of this magnitude on such a product.

Becoming an associate of Usana International costs anywhere from $19.95 to $49.95 which covers the starter kit. Out of the list of MLM companies in Singapore there are several who are free to join, but cost income for starter kits. Nothing uncommon at all, but if you are on a financial budget you will want to research each company and find out which is the best for you. Just remember strong research equals greater confidence in the company you choose.