Final answer:
The sample mean of 4.4 cm with a standard deviation of 3.61 cm, when compared to the population mean of 4.25 cm, seems probable to originate from the said population, especially given the law of large numbers and a small calculated standard error of approximately 0.114 cm.
Step-by-step explanation:
Whether the sample is from the indicated population depends on comparing the sample mean to the population mean while considering the variability of the sample means, known as the standard error. Since our sample mean is 4.4 cm, which is reasonably close to the population mean of 4.25 cm, and considering the law of large numbers, the sample mean should be close to the population mean for large sample sizes.
The standard deviation of the sample is given as 3.61 cm, the same as the population standard deviation. The difference between the sample mean and the population mean can be assessed by determining how many standard errors away it is. The standard error is the population standard deviation divided by the square root of the sample size. Here, it would be 3.61 cm / √1000, which yields a standard error of approximately 0.114 cm.
The difference between our sample mean and population mean is 4.4 - 4.25 = 0.15 cm, which is roughly 1.32 standard errors away (0.15 cm / 0.114 cm per standard error). Typically, we would look to a z-score table or statistical software to determine the probability of observing such a sample mean from the population described, but this information is not given. However, if we apply the empirical rule and the central limit theorem, this difference is well within 2 standard deviations from the mean; thus, it is likely that our sample could come from the population specified, unless there is further evidence suggesting otherwise.