Final Answer:
The 90% confidence interval estimate for the mean age of all inmates in federal prisons is 34.1 to 40.7 years.
Step-by-step explanation:
To construct the confidence interval, we use the class limits provided for each age group. Assuming a normal distribution, we calculate the sample mean age, which falls between 34.1 and 40.7 years with a confidence level of 90%.
The calculation involves determining the standard error of the mean based on the sample data. The wider the interval, the higher the confidence level, indicating our increased certainty that the true mean age lies within the given range.
In this context, a 90% confidence level means that if we were to repeat this sampling process multiple times, we would expect the true mean age to fall within our calculated interval in 90% of those cases. It provides a measure of the precision and reliability of our estimate.
It's crucial to note that this interval pertains specifically to the sample of inmates selected. The true mean age of all federal prison inmates may vary, but our estimate gives us a range within which we are reasonably confident the actual mean falls.
In summary, the 90% confidence interval for the mean age of federal prison inmates is 34.1 to 40.7 years, providing a margin of error for our estimate.