A statistician uses maximum likelihood estimation for a normal distribution. For a sample of 25 observations with mean 100 and known population standard deviation 5, what is the MLE of the population mean?

Tue, 05 May 2026 22:35:55 +0000

A statistician uses maximum likelihood estimation for a normal distribution. For a sample of 25 observations with a mean of 100 and a known population standard deviation of 5, what is the MLE of the population mean? This question reflects growing curiosity among data professionals about reliable methods for estimating key parameters, especially in scientific and business applications. At first glance, the math might seem abstract—but understanding maximum likelihood estimation offers clarity on how data leads to precise inferences. ### Why Maximum Likelihood Estimation Matters Now In today’s data-driven United States landscape, accurate statistical inference underpins decision-making across fields—from healthcare research to financial forecasting. When researchers analyze real-world samples, they often rely on MLE because it delivers consistent, efficient estimates even with limited data. As predictive modeling and data analytics evolve, the clarity and rigor of MLE reinforce its role in producing trustworthy results from normal distribution-based samples.