If you assume the normal model for these data, N(0.18, 0.04), in about what percentage of counties would the proportion of people 65 and older be more than 0.22?
To find the percentage of counties where the proportion of people 65 and older is more than 0.22, we can use the normal distribution and its associated z-score.
Step 1: Calculate the z-score.
The z-score formula is given by: (value - mean) / standard deviation
In this case, the value is 0.22, the mean is 0.18, and the standard deviation is 0.04.
So, the z-score is: (0.22 - 0.18) / 0.04 = 1
Step 2: Lookup the z-score.
We need to find the percentage of counties where the z-score is greater than 1. We can use a standard normal distribution table or a calculator to find the percentage associated with this z-score.
By using a standard normal distribution table or a z-score calculator, we can determine that the percentage of counties where the z-score is greater than 1 is approximately 0.1587 or 15.87%.
Therefore, in about 15.87% of counties, the proportion of people 65 and older would be more than 0.22.