Practice Sampling Distribution in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The probability distribution of a statistic (such as the sample mean) computed from all possible random samples of the same size drawn from a population.
Imagine you survey 50 random people about their height, compute the average, then repeat with a different group of 50, again and again. Each group gives a slightly different average. The pattern of all those averages forms the sampling distribution. It's like taking the temperature of a city by sending out 100 different thermometers—each reads slightly differently, but together they cluster around the truth.
Example 1
mediumA population has \mu=50 and \sigma=12. For random samples of size n=36, describe the sampling distribution of \bar{X}: find its mean, standard error, and shape.
Example 2
hardFor a population with \mu=100, \sigma=20, and n=25: (a) find P(\bar{X} > 104), (b) find the value c such that P(\bar{X} < c) = 0.90.
Example 3
easyThe standard error of a sample mean is \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}. If \sigma=10 and n=100, find the standard error. What happens to the SE if n is quadrupled to 400?
Example 4
hardA population proportion is p=0.40. For samples of size n=100, describe the sampling distribution of \hat{p} and find P(\hat{p} > 0.45).