Question

​jody, a statistics​ major, grows tomatoes in her spare time. she measures the diameters of each tomato. assume the normal model is appropriate. one tomato was in the 50th percentile. what was its​ z-score?

Answer 1

Refer to the attached Z Table: (Credit to UFL Stat Dep)
 http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

There are two charts: one consisting of negative z values and another consisting of positive z values. The negative z values correspond to values on the left side of the normal curve (below the 50th Percentile). The positive z values correspond to the values on the right side of the normal curve (above 50th percentile).

If the further below the 50th percentile we get, the larger the negative number gets for z, and the further above the 50th percentile we get, the larger the positive number is for z, what do you think the z score of a tomato that is exactly on the 50th percentile is?

Referring to the chart (find .5000) for both the negative and positive z values, your intuition is confirmed: the z-score is 0.