The heights of male students in a given university are normally distributed, with a mean of 70 inches and a standard deviation of .5 inches. Find the height (x value) that corresponds to the z value of -1.33.
z = (x - mean)/standard deviation
find x
To find the height (x value) that corresponds to the z value of -1.33, we will use the formula for standardizing a normally distributed variable:
z = (x - μ) / σ
where z is the z score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, we are given the z score (-1.33), the mean (70 inches), and the standard deviation (0.5 inches). We can rearrange the formula to solve for x:
x = z * σ + μ
Plugging in the given values:
x = -1.33 * 0.5 + 70
Simplifying:
x = -0.665 + 70
x ≈ 69.335
Therefore, the height (x value) that corresponds to the z value of -1.33 is approximately 69.335 inches.