Final Answer:
In a random sample of 55 nonfarm workers, approximately 9.92 workers (rounded to the nearest hundredth) are expected to be government employees based on the reported rate of 17 out of 4.5 nonfarm workers being government employees.
Step-by-step explanation:
To determine the expected number of government employees in a random sample of 55 nonfarm workers, we first calculate the proportion of government employees to nonfarm workers based on the reported rate. The rate provided is 17 government employees for every 4.5 nonfarm workers. To find the proportion for a single nonfarm worker, we divide 17 by 4.5, resulting in approximately 3.78 government employees per nonfarm worker.
Next, to find the expected number of government employees in the sample of 55 workers, we multiply the proportion by the total number of workers in the sample. Multiplying 3.78 by 55 yields approximately 208.27 government employees. However, since we cannot have a fraction of a worker, we round this number to the nearest whole number, which is 9.92 when rounded to the nearest hundredth.
Therefore, based on the reported rate of government employees among nonfarm workers, we expect approximately 9.92 workers out of the 55 in the random sample to be government employees. This calculation helps estimate the proportion of government employees in a given sample, providing valuable insights into workforce compositions and trends.