normal distribution

normal 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 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

  We show you through an example how to work out probabilities from a normal distribution. A battery has a lifetime which is normally distributed with a mean of 62 hours and a standard deviation of 3 hours. What is the probability of a battery lasting less than 68 hours?

  Exploring the normal distribution

Question : According to statistics, returns from the 2008 filing season show an average income tax refund of 2383. If the standard deviation of income tax returns 1525 and the distribution of refunds is approximately normal. 1. What is the probability that a return selected at random resulted in the taxpayer receiving a refund? 2. Of returns of this type, 10% will receive a refund of what amount or less?

Answer : To solve problems like this, you need a z-table (or a calculator that can compute the numbers). Here is a link to a z table: http://lilt.ilstu.edu/dasacke/eco148/ZTable.htm So we have a mean of 2383 and std dev 1525 1.) We want to know how many people had a refund (that is, a return greater than 0) Standardize the score 0 as (0-2383)/1525 = -1.5626 Now lookup that score in the z table and you get 0.0594 as the probability of getting less than -1.5626. We want to know how many people did better than that, so the probability is 1 - 0.0594 = .9406 2.) What is the 10th pecentile? Find 0.1 in the z table and lookup backwards what score it came from, you get -1.28 so thats a refund of 2383 - (1525)*1.28 = 431..   More from Yahoo Answers

Question : In what ways is the t distribution similar to the standard normal distribution? In what ways is the t distribution different from the standard normal distribution? How does the formula for the t test differ from the formula for the z test?

Answer : The overall shape of the probability density function of the t-distribution resembles the bell shape of a normally distributed variable with mean 0 and variance 1, except that it is a bit lower and wider...   More from Yahoo Answers