normal probability distribution

normal probability distribution : In probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that describes data that clusters around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve. The normal distribution can be used to describe, at least approximately, any variable that tends to cluster around the mean. For example, the heights of adult males in the United States are roughly normally distributed, with a mean of about 70 inches. Most men have a height close to the mean, though a small number of outliers have a height significantly above or below the mean. A histogram of male heights will appear similar to a bell curve, with the correspondence becoming closer if more data is used. For theoretical reasons (such as the central limit theorem), any variable that is the sum of a large number of independent fac....   More from Wikipedia

normal probability distribution : \int_{-\infty}^{\alpha\left(\frac{x-\xi}{\omega}\right)} e^{-\frac{t^2}{2}}\ dt |}} In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Let $\backslash phi(x)$..   More from Wikipedia

  In this tutorial we show you how to calculate the probability given that x is less than the mean from a normal distribution by looking at the following example. A carton of orange juice has a volume which is normally distributed with a mean of 120ml and a standard deviation of 1.8ml. Find the probability that the volume is more than 118ml.

  Review of the normal density function and its key properties

Question : Mean life a refrigerator follows a Normal Distribution with a mean of 7.2 years and a standard deviation of 1.9 years. What fraction of the refrigerator last more than 10 Years? Can you explain how you come up with your answer?

Answer : Dear shavon60120, When solving this type of problem, you need to either have a calculator that gives you values from the normal distribution or look them up in tables. Tables are usually standardized, meaning they are for a normal distribution with a mean of 0 and a standard deviation of 1. If you are using standardized normal tables, you can put the numbers in your problem into standardized form by shifting and rescaling the particular normal distribution you start with. This is done by first subtracting the mean from your quantity of interest (this does the shifting), and then dividing this result by the standard deviation (this does the rescaling). Thus, for your problem, where x = 10 years is your quantity of interest, m = 7.2 years is the mean, and d = 1.9 years is the standard deviation, you get z = (x - m) / d = (10 - 7.2) / 1.9 = 2.8 / 1.9 = 1.47368 (to five decimal places). The quantity z now represents the number of standard deviations that your quantity is abo....   More from Yahoo Answers

Question : has a normal probability distribution a. for only large sample sizes b. for aonly small sample sizes c. for any sample size d. for only sample sizes greater or equal to 30 e. none of the above answers is correct

Answer : The answer is D. Most statisticians consider a sample of 30 or more to be large enough for the central limit theorem to be employed. Look closely in your textbook and you'll probably find the statement you just typed, word for word, verbatim. Good luck in your studies, ~ Mitch ~ Edit: After reading "WantingtoKnow's" answer, I would agree with his statement. As a result, I gave him a thumbs up. Therefore, the answer should be "C"...   More from Yahoo Answers

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