When tossing two dice and finding the mean, X we find that has a mean or expected value, and a standard deviation

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Please help me find the mean and standard deviation

We found that the mean is μ = 3.5 and the standard deviation is σ = 1.7078.

Now, suppose that instead of tossing one die and counting the number of dots facing up we toss two dice and let \(\overline{X}\) = the mean number of dots facing up on the two dice.

Note that when tossing 2 dice, \(\overline{X}\) could end up being 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, or 6.0.

\(\overline{X}\) is a random variable. We call the expected value (also known as the mean) of this random variable E(\(\overline{X}\)) or μ\(_{\overline{X}}\). Your text uses the symbol μ\(_{\overline{X}}\).

The standard deviation of \(\overline{X}\), also called the standard error of the mean is denoted by the symbol σ\(_{\overline{X}}\). It is easy to calculate once you know σ, which you found on MAC15. Review Chapter 7 if you’ve forgotten the formula. Then complete the following sentence:

When tossing two dice and finding the mean, \(\overline{X}\), we find that \(\overline{X}\) has a mean or expected value,

μ\(_{\overline{X}}\) = ________ and a standard deviation σ\(_{\overline{X}}\) = ________.
Transcribed Image Text:We found that the mean is μ = 3.5 and the standard deviation is σ = 1.7078. Now, suppose that instead of tossing one die and counting the number of dots facing up we toss two dice and let \(\overline{X}\) = the mean number of dots facing up on the two dice. Note that when tossing 2 dice, \(\overline{X}\) could end up being 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, or 6.0. \(\overline{X}\) is a random variable. We call the expected value (also known as the mean) of this random variable E(\(\overline{X}\)) or μ\(_{\overline{X}}\). Your text uses the symbol μ\(_{\overline{X}}\). The standard deviation of \(\overline{X}\), also called the standard error of the mean is denoted by the symbol σ\(_{\overline{X}}\). It is easy to calculate once you know σ, which you found on MAC15. Review Chapter 7 if you’ve forgotten the formula. Then complete the following sentence: When tossing two dice and finding the mean, \(\overline{X}\), we find that \(\overline{X}\) has a mean or expected value, μ\(_{\overline{X}}\) = ________ and a standard deviation σ\(_{\overline{X}}\) = ________.
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