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?
Z = (score-mean)/SD
Insert the values and calculate.
To find the z-value for a given height (x), we can use the formula:
z = (x - μ) / σ
where:
- x is the given height
- μ is the mean height of the population
- σ is the standard deviation of the population
In this case:
- x = 67 inches (the given height)
- μ = 65 inches (the mean height of the population)
- σ = 1.5 inches (the standard deviation of the population)
Plugging in these values into the formula:
z = (67 - 65) / 1.5
z = 2 / 1.5
z = 1.33 (rounded to two decimal places)
So, the z-value for a height of 67 inches is approximately 1.33.
To find the z-value for a given height (x), you can use the formula:
z = (x - mean) / standard deviation
Given:
Mean height (mean) = 65 inches
Standard deviation (σ) = 1.5 inches
Height (x) = 67 inches
Substituting these values into the formula, we get:
z = (67 - 65) / 1.5
Calculating this equation, we have:
z = 2 / 1.5
Therefore, the z-value for a height of 67 inches is approximately 1.33.