Despite he outrageous incomes of some, the mean income of all aging rock stars is relatively modest: $75,000 with a standard deviation of $2,000. On that scale, Chubby Checker, appears to do better than average: at most, only 6.25% of aging rockers make more than he does. what is Chubby Checkers income?
http://davidmlane.com/hyperstat/z_table.html
Here is process:
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.0625) and its Z score. Insert data into above equation and solve for score.
To find Chubby Checker's income, we need to determine the value corresponding to the top 6.25% of incomes in the distribution. We can achieve this by using the standard deviation and mean.
1. First, we need to find the Z-score associated with the percentile (6.25%). The Z-score represents the number of standard deviations an observation is away from the mean. We can calculate the Z-score using the standard normal distribution table or a calculator. For 6.25%, the Z-score is approximately -1.96.
2. Next, we use the formula for Z-score:
Z = (X - mean) / standard deviation
Rearranging the formula, X (income) can be calculated as:
X = Z * standard deviation + mean
Plugging in the values, we get:
X = -1.96 * 2000 + 75000
Calculating this equation, we find:
X ≈ 75000 - 3920 = 71080
Therefore, Chubby Checker's income is approximately $71,080.