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Normality can be used for acid-base titrations. For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be ...
Student's t-test assumes that the sample means being compared for two populations are normally distributed, and that the populations have equal variances.Welch's t-test is designed for unequal population variances, but the assumption of normality is maintained. [1]
Simple back-of-the-envelope test takes the sample maximum and minimum and computes their z-score, or more properly t-statistic (number of sample standard deviations that a sample is above or below the sample mean), and compares it to the 68–95–99.7 rule: if one has a 3σ event (properly, a 3s event) and substantially fewer than 300 samples, or a 4s event and substantially fewer than 15,000 ...
Bailey and Crandall show an explicit uncountably infinite class of b-normal numbers by perturbing Stoneham numbers. It has been an elusive goal to prove the normality of numbers that are not artificially constructed. While √ 2, π, ln(2), and e are strongly conjectured to be normal, it is still not known whether they are normal or not.
Newton's method is ideal to solve this problem because the first derivative of (), which is an integral of the normal standard distribution, is the normal standard distribution, and is readily available to use in the Newton's method solution.
Standard solutions are generally prepared by dissolving a solute of known mass into a solvent to a precise volume, or by diluting a solution of known concentration with more solvent. [1] A standard solution ideally has a high degree of purity and is stable enough that the concentration can be accurately measured after a long shelf time. [2]
The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).
Asymptotic normality, in mathematics and statistics; Complete normality or normal space, Log-normality, in probability theory; Normality (category theory) Normality (statistics) or normal distribution, in probability theory; Normality tests, used to determine if a data set is well-modeled by a normal distribution