Answer to Question #345022 in Statistics and Probability for Dan

Question #345022

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.

1
Expert's answer
2022-05-26T15:53:02-0400



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}"

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