if income in the US was normally distributed, what z-score would represent the bottom 10%, the poorest 10%
I have a table of z versus F(z)
it shows for F(z) = .1 or 10 %, z = -1.3 or 1.3 standard deviations below mean
I studied Spanish from a book entitled "El Camino Real" when I was in the 8th grade more than 65 years ago. I wonder how anyone would guess from this post title that the problem was one in statistics?
To find the z-score that represents the bottom 10% (poorest 10%) of the income distribution in the US, you would need to use the standard normal distribution table or a statistical software. Here's how you can go about it:
Step 1: Standardize the data: Convert the income value to a standardized Z-score using the formula:
Z = (X - μ) / σ
Where:
Z is the standard score (Z-score)
X is the raw score (income value)
μ is the mean of the distribution (average income)
σ is the standard deviation of the distribution
Step 2: Use the standard normal distribution table: Look up the cumulative probability value closest to 10% in the body of the table or use a statistical software to find the corresponding Z-score. Remember that the table provides probabilities for positive Z-scores, so you may have to work with the complement (1 - 10% = 90%) depending on the table or software you are using.
Step 3: Interpret the Z-score: The obtained Z-score would represent the number of standard deviations below the mean income that corresponds to the bottom 10% of the distribution. A negative Z-score means that the income is below the mean.
Since the mean and standard deviation of income data in the US can vary over time, it would be challenging to give you an exact Z-score without specific information about the mean and standard deviation of the income distribution you are referring to.