Question
If a normal distribution shows that the height of adult women has a mean of 64.5 inches and a standard deviation of 2.5 inches, what does a z-score of -1.4 mean?
Answers
GPT 3.5
A z-score is a measure of how many standard deviations a particular data point is from the mean of a distribution.
In this case, a z-score of -1.4 indicates that a data point is 1.4 standard deviations below the mean.
To calculate the corresponding height, we will use the formula:
z = (x - μ) / σ
Rearranging the formula, we have:
x = μ + (z * σ)
Substituting the given values:
x = 64.5 + (-1.4 * 2.5)
x = 64.5 - 3.5
x = 61
Therefore, a z-score of -1.4 indicates that the height of an individual is 61 inches, which is 1.4 standard deviations below the mean height of adult women.
In this case, a z-score of -1.4 indicates that a data point is 1.4 standard deviations below the mean.
To calculate the corresponding height, we will use the formula:
z = (x - μ) / σ
Rearranging the formula, we have:
x = μ + (z * σ)
Substituting the given values:
x = 64.5 + (-1.4 * 2.5)
x = 64.5 - 3.5
x = 61
Therefore, a z-score of -1.4 indicates that the height of an individual is 61 inches, which is 1.4 standard deviations below the mean height of adult women.