Examples of zvalue in the following topics:

 A common mistake is to look up a zvalue in the table and simply report the corresponding entry, regardless of whether the problem asks for the area to the left or to the right of the zvalue.
 The table only gives the probabilities to the left of the zvalue.
 There is another note of caution to take into consideration when using the table: The table provided only gives values for positive zvalues, which correspond to values above the mean.
 What if we wished instead to find out the probability that a value falls below a zvalue of 0.51, or 0.51 standard deviations below the mean?
 This table can be used to find the cumulative probability up to the standardized normal value z.

 Standard scores are also called zvalues, zscores, normal scores, and standardized variables.
 The use of "Z" is because the normal distribution is also known as the "Z distribution".
 The zscore is only defined if one knows the population parameters.
 The absolute value of z represents the distance between the raw score and the population mean in units of the standard deviation.
 The Z value measures the sigma distance of actual data from the average and provides an assessment of how offtarget a process is operating.

 A normal probability table, which lists Z scores and corresponding percentiles, can be used to identify a percentile based on the Z score (and vice versa).
 Generally, we round Z to two decimals, identify the proper row in the normal probability table up through the ﬁrst decimal, and then determine the column representing the second decimal value.
 We can also ﬁnd the Z score associated with a percentile.
 For example, to identify Z for the 80th percentile, we look for the value closest to 0.8000 in the middle portion of the table: 0.7995.
 We determine the Z score for the 80th percentile by combining the row and column Z values: 0.84.

 Thus, a positive zscore represents an observation above the mean, while a negative zscore represents an observation below the mean.
 Zscores are also called standard scores, zvalues, normal scores or standardized variables.
 The use of "z" is because the normal distribution is also known as the "z distribution.
 The absolute value of z represents the distance between the raw score and the population mean in units of the standard deviation.
 Define zscores and demonstrate how they are converted from raw scores.

 The greater the value of ρ, the more pronounced the skew.
 The variable is called z' and the formula for the transformation is given below.
 What is important is that z' is normally distributed and has a standard error of
 The first step is to convert both 0.60 and 0.75 to their z' values, which are 0.693 and 0.973, respectively.
 The standard error of z' for N = 12 is 0.333.

 To find the kth percentile when the zscore is known: k = µ + ( z ) σ

 The standard normal distribution is a normal distribution of standardized values called zscores.
 For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standard deviations above (or to the right of) the mean.
 x = µ + ( z ) σ = 5 + ( 3 )( 2 ) = 11 (6.1)
 The transformation z = (x − µ)/σ produces the distribution Z ∼ N ( 0,1 ) .
 The value x comes from a normal distribution with mean µ and standard deviation σ.

 Taking the first interval as an example, we want to know the z value such that 0.1 of the area in the normal distribution is below z.
 Therefore, 10% of the distribution is below a z value of 1.28.
 Let the cumulative distribution function of the normal density be denoted by Φ(z).
 Likewise, we expect Φ(z(2)) to take on a value in the interval (1/n, 2/n).
 Continuing, we expect Φ(z(n)) to fall in the interval ((n  1)/n, 1/n).

 If it is 1.5 standard deviations below the mean, then its Z score is 1.5.
 Using µSAT = 1500, σSAT = 300, and xAnn = 1800, we ﬁnd Ann's Z score:
 Observations above the mean always have positive Z scores while those below the mean have negative Z scores.
 SAT score of 1500), then the Z score is 0.
 One observation x1 is said to be more unusual than another observation x2 if the absolute value of its Z score is larger than the absolute value of the other observation's Z score: Z1 > Z2.

 The zscore tells you how many standard deviations that the value x is above (to the right of) or below (to the left of) the mean, µ.
 Values of x that are larger than the mean have positive zscores and values of x that are smaller than the mean have negative zscores.
 If x equals the mean, then x has a zscore of 0.
 Summarizing, when z is positive, x is above or to the right of µ and when z is negative, x is to the left of or below µ.
 The zscore allows us to compare data that are scaled differently.