In solving this problem, the relevant distribution is specified: x is N(4,16). We want to find the probability that the selected element has a value less than 3.0 or greater than 6.1.

Suppose the underlying population of elements is N(4,16) and one element from this population is selected. P ercentiles smaller than the 50 th percentile can be found by noting that the G aussian distribution is symmetric about zero so that, for example, z 0.30=в€’0.524. a T his table was generated with MINITAB R elease 14.13 as follows: T he indicated cumulative probabilities 0.5 to 0.99999 were placed in a column of a MINITAB worksheet and the following commands given: b E xample: T he 75 th percentile, or the z value below, which is 75% of the G aussian distribution, equals 0.674, z 0.75=0.674. Within the N ormal Distribution dialog box, I nverse cumulative probability was selected, M ean was set to 0.0, S tandard deviation was set to 1.0, and the column of the worksheet containing the cumulative probabilities was selected and placed in the I nput column: followed by hitting OK. Table 1-2 provides an example of such a table and gives the percentiles of the standard Gaussian distribution.Д¬ alc ( from the main menu of MINITAB)в†’ P robability D istributionsв†’ N ormal Distribution. That all Gaussian distributions can be transformed to the standard Gaussian distribution is convenient in that just a single table is required to summarize the probability structure of the infinite number of Gaussian distributions.

The elements of the standard Gaussian distribution are traditionally designated by the letter z so that it can be said that z is N(0,1). The distribution of a standardized Gaussian distribution-that is, a Gaussian distribution that has its elements standardized in this form-has its center at zero and has a variance of unity. Standardization in general is accomplished by subtracting the center of the distribution from a given element in the distribution and dividing the result by the standard deviation of the distribution.

All Gaussian distributions can be standardized to the reference Gaussian distribution, which is called the standard Gaussian distribution.

Gaussian software labels