Answer :
The mean of the sampling distribution is 156 lb, and the standard error of the mean is approximately 8.69 lb when using random samples of size 7.
The mean of the sampling distribution remains equal to the population mean, which is 156 lb, reflecting the property of sampling distributions to preserve the population mean. However, the standard error of the mean, representing the variability of sample means around the population mean, is calculated as the population standard deviation divided by the square root of the sample size. In this case, the standard error of the mean is approximately 2377
23, resulting in a value of approximately 8.69 lb when rounded to the nearest hundredth. The standard error of the mean indicates the precision of the sample mean as an estimator of the population mean, with smaller values indicating greater precision.
Therefore, in random samples of size 7 from this population, the average deviation of sample means from the population mean is approximately 8.69 lb. This information is crucial for understanding the reliability and accuracy of sample means in estimating the population parameter, providing valuable insights for statistical inference and decision-making based on sample data.
