Examples of zscore in the following topics:

 If the observation is one standard deviation above the mean, its Z score is 1.
 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.




 If the observations are normally distributed, then their Z scores will approximately correspond to their percentiles and thus to the zi in Table 3.16.

 Example 3.7 Ann from Example 3.2 earned a score of 1800 on her SAT with a corresponding Z = 1.
 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).
 We use this table to identify the percentile corresponding to any particular Z score.
 We can also ﬁnd the Z score associated with a percentile.
 We determine the Z score for the 80th percentile by combining the row and column Z values: 0.84.

 For the following data, plot the theoretically expected z score as a function of the actual z score (a QQ plot).

 Cumulative SAT scores are approximated well by a normal model, N(µ = 1500,σ = 300).
 The simplest way to ﬁnd the shaded area under the curve makes use of the Z score of the cut oﬀ value.
 With µ = 1500, σ = 300, and the cutoﬀ value x = 1630, the Z score is computed as
 However, the percentile describes those who had a Z score lower than 0.43.
 The probability Shannon scores at least 1630 on the SAT is 0.3336.


 This will be useful in a wide range of practical settings, especially when trying to make a quick estimate without a calculator or Z table.