# Calculating Z-Score and Standard Deviation

Learning Goal: I’m working on a statistics multi-part question and need an explanation and answer to help me learn.

The average height for all males is 69.3 inches with a standard deviation of 2.8 inches. For females, the average height is 64 inches and the standard deviation is 2.8. These are population values. For this week’s discussion, you will calculate a z-score based on your own height and determine whether your score is within the 95% normal range or if it is out of that range and considered unusual.

• Measure your height as precisely as possible to a tenth of an inch. For example, 5’2 ¼” would be 62.3 inches tall.
• Calculate the z-score based on population values for males or females. Use the formula: z= (x-µ)/σ where x is your height in inches.
• Calculate the normal range by creating the interval that is within 2 standard deviations of the population mean. Multiply the population standard deviation by 2 and then add/subtract from the population mean.

• Is your height within the normal range? Is this what you expected?
• Would your height be considered unusual? Why or why not.
• Have you encountered any challenges based on your height? For example, someone who is shorter or taller may have a difficult time finding pants that are an appropriate length.
• How is the concept of normality used in your field? Example: a patient’s blood pressure is compared to a normal range of values and a financial planner may check the “average” return of a stock.
• How does knowing what is usual help people and corporations and government organizations plan? For example, how do airplane manufacturers use the normal height to design aircraft seating?
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