Don't worry - we don't have to perform this integration - we'll use the computer to do it for.

Assume that the lives of the motors follow a normal distribution.

X found in a particular interval a, b is the area under the curve bounded by x a and x b and is given.

The cumulative distribution function is given by: X is the random variable.

To the right of 2 desktop image mac os x will be represented by the area from x_113/6 2 1/6.167 to x_28/3 2 2/3.667.Normal Distribution Standard Deviation Quincunx Probability and Statistics Menu.Show answer Example 4 Find the following probabilities: (a) P (.06) (b) P ( Z -2.15) (c) P (1.06.00) (d) P (-1.06.00) Show answer Example 5 It was found that the mean length of 100 parts produced.Note: In a normal distribution, only 2 parameters are needed, namely and.Standard normal distribution table z ( z ) ( z ).00.5000.3989.01.5040.3989.02.5080.3989.03.5120.3988.04.5160.3986.05.5199.3984.06.5239.3982.07.5279.3980.08.5319.3977.09.5359.3973.10.5398.3970.11.The z -Table The areas under the curve bounded by the ordinates z 0 and any positive value irepo x para windows of z are found in the z -Table.

If we have the standardized situation of 0 and 1, then we have: f(X)1 sqrt(2pi)e(-x2 2 We can transform all the observations of any normal random variable X with mean and variance to a new set of observations of another normal random variable Z with.

Normal distribution is a continuous probability distribution.

You can explore the concept of the standard normal curve and the numbers in the z-Table using the following applet.This random variable, x is said to be normally distributed with mean and standard deviation if its probability distribution is given by 2 sigma2, properties of a Normal Distribution, the normal curve is symmetrical about the mean ; The mean is at the middle and.The shaded area represents the probability of an event with mean, standard deviation occuring between x 1 and.Try setting mu0 and sigma1 for the green curve.(Example of how to use is below).The upper gray line is 2 standard deviations above the mean and the lower gray line is 2 standard deviations below the mean.Standardizing the distribution like this makes it much easier to calculate probabilities.Standard normal distribution table is used to find the area under the f ( z ) function in order to find the probability of a specified range of distribution.The probability of a continuous normal variable.

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### Normal probability distribution z table

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