MediumStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Learning from Samples Statistics Basics › Data and SamplingNumerical

Three fair dice are thrown, and x is the mean of the three faces…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Three fair dice are thrown, and $\bar x$ is the mean of the three faces. A single die has mean $3.5$ and population standard deviation about $1.708$ . Find the mean of the sampling distribution of $\bar x$ . Find its standard error to three decimal places. Find the probability that $\bar x$ is at least $5$ , to four decimal places.

Need a reminder? The key ideaShow

The sampling distribution of $\bar x$ is centred at $\mu$ . Its standard error is

\displaystyle SE = \dfrac{\sigma}{\sqrt{n}}.

For larger samples it is close to a normal curve, so about $95\%$ of sample means lie within $2$ standard errors of $\mu$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A machine fills bags of rice. The masses of single bags have a standard deviation of 15 g…A spinner shows 1, 2 or 6, each with the same chance… →

More onStatistics Basics › Learning from Samples Statistics Basics › Data and Sampling

Discussion (0)

Loading…