3. Describing z-scores

Pica is a disorder in which individuals eat substances that are typically non-nutritive or inedible, such as dirt, paint chips, ice or frost, clay, paper, and so forth. To be diagnosed with pica, these cravings need to last longer than a month and be developmentally inappropriate. Pica is seen in all ages, but more commonly among pregnant women, small children, and those with developmental disabilities. Pica can lead to serious medical problems, particularly when the substance ingested can lead to poisoning (such as lead poisoning from paint chips), parasites (for example, from soil), or intestinal blockages. [Source: American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders.4th ed. Text rev. (Washington, DC: American Psychiatric Association, 2000).]

A medical researcher is studying the relationship between pica and iron deficiency. He measures the hemoglobin levels in five of his patients, all of whom are adult females who have been diagnosed with pica. He wants to compare these levels to the population norms. Suppose the mean hemoglobin level in adult females is 13.2 gm/dl with a standard deviation of 1.2 gm/dl. The researcher compiles the following table, where the first column of values is the patient's hemoglobin level (Hb level), the second column describes the location of that hemoglobin level in the distribution of hemoglobin levels among adult females, and the third column contains the corresponding z-score of that patient's hemoglobin level. Fill in the missing values.

	Hb Level (gm/dl)	Location Description	z-score
Patient 1	10.8	two standard deviations below the mean
Patient 2	13.8		+0.50
Patient 3		one-quarter of a standard deviation above the mean
Patient 4	9.6		-3.00
Patient 5		one standard deviation below the mean	-1.00