Answer to Question #345020 in Statistics and Probability for Dan

Question

Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.

Answer 1

Sampling distribution of the sample mean:

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & \bar{X} & f & f(\bar{X}) & Xf(\bar{X})& X^2f(\bar{X}) \\ \hline & 16.5 & 1 & 0.1 & 1.65 & 27.225\\ \hdashline & 17 & 1 & 0.1 & 1.7 & 28.9\\ \hdashline & 17.5 & 2 & 0.2 & 3.5 & 30.625\\ \hdashline & 18& 2 & 0.2 & 3.6 &32.4\\ \hdashline & 18.5& 2 & 0.2 & 3.7& 34.225\\ \hdashline & 19& 1 & 0.1 & 1.9 & 36.1 \\ \hdashline &19.5 & 1& 0.1& 1.95&38.025 \\ \hdashline Total= & & 10 & 1 & 18 & 227.5 \\ \hdashline \end{array}$$