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steposvetlana [31]
3 years ago
6

In one popular game, five number cubes are rolled at the same time. if the number cubes are kept separate, what is the total pos

sible number of outcomes
Mathematics
1 answer:
madreJ [45]3 years ago
3 0

5 cubes, each have six sides containing different numbers = 6⁵   = 7,776

Answer: 7,776 total possible outcomes


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i) 2 - 1.64 \frac{0.1}{\sqrt{16}}= 1.959  

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So then the 90% confidence interval is given by (1.959, 2.041)

ii) Figure attached

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval is given by this formula:

\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}}   (1)

And for a 90% of confidence the significance is given by \alpha=1-0.9=0.1, and \frac{\alpha}{2}=0.05. Since we know the population standard deviation we can calculate the critical value z_{0.05}= \pm 1.64

We know the folllowing data:

\bar X = 2 represent the sample mean

\sigma = 0.1 represent the population deviation

n =16 represent the sample size

Part i)

If we replace the values given into formula (1) we got:

2 - 1.64 \frac{0.1}{\sqrt{16}}= 1.959  

2 + 1.64 \frac{0.1}{\sqrt{16}}= 2.041  

So then the 90% confidence interval is given by (1.959, 2.041)

Part ii)

Figure attached. We have the illustration for the confidence interval obtained.

Part iii)

The margin of error is given by:

ME=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}}

And if we replace we got:

ME= 1.64 *\frac{0.1}{\sqrt{16}}= 0.041

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