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 values and calculate.
To find the z-value for a given height of 67 inches, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the given height
- μ is the mean height
- σ is the standard deviation
In this case:
x = 67 inches
μ = 65 inches
σ = 1.5 inches
Substituting these values into the formula, we get:
z = (67 - 65) / 1.5
Simplifying this equation, we have:
z = 2 / 1.5
z = 1.33
Therefore, the z-value for a height of 67 inches is 1.33.
To find the z-value for a given height, we can use the formula:
z = (x - μ) / σ
where:
- z is the z-value
- x is the value we want to convert to a z-score
- μ is the mean of the population
- σ is the standard deviation of the population
In this case, the mean height (μ) is 65 inches, the standard deviation (σ) is 1.5 inches, and we want to find the z-value for a height (x) of 67 inches.
Let's plug these values into the formula:
z = (67 - 65) / 1.5
Simplifying this calculation, we get:
z = 2 / 1.5
z ≈ 1.33
So, the z-value for a height of 67 inches is approximately 1.33.