The distribution of heights of American women aged 18 to 24 is approximately normally distributed with a mean of 65.5 inches and a standard deviation of 2.5 inches. Calculate the z-score for a woman six feet tall.
To calculate the z-score for a woman who is six feet tall (72 inches):
Step 1: Calculate the z-score formula:
z = (x - μ) / σ
where:
x = individual value (height in this case),
μ = mean value (65.5 inches),
σ = standard deviation (2.5 inches).
Step 2: Substitute the given values into the formula:
z = (72 - 65.5) / 2.5
Step 3: Calculate:
z = 6.5 / 2.5
Step 4: Simplify:
z = 2.6
Therefore, the z-score for a woman who is six feet tall is 2.6.
To calculate the z-score for a woman who is six feet tall, we first need to convert her height from feet to inches. Since there are 12 inches in a foot, we have:
6 feet * 12 inches/foot = 72 inches
Next, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where:
- z is the z-score
- x is the value we want to standardize (in this case, 72 inches)
- μ is the mean (65.5 inches)
- σ is the standard deviation (2.5 inches)
Plugging in the values:
z = (72 - 65.5) / 2.5
z = 6.5 / 2.5
z = 2.6
Therefore, the z-score for a woman who is six feet tall (72 inches) is 2.6.