Suppose the mean height of a population is 65 inches with a standard deviation of 1.5 inches. What is the z value for a height (x) of 67 inches?
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To find the z-value (also known as standard score) for a given height, you can use the formula:
z = (x - μ) / σ
where:
- z is the standard score
- x is the given value
- μ is the mean of the population
- σ is the standard deviation of the population
In this case, the given height (x) is 67 inches, the mean (μ) is 65 inches, and the standard deviation (σ) is 1.5 inches. Plugging in these values into the formula, we get:
z = (67 - 65) / 1.5
Simplifying the equation:
z = 2 / 1.5
z ≈ 1.3333
Therefore, the z-value for a height of 67 inches in this population is approximately 1.3333.