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# Rolling a fair ten dash sided ten-sided die produces a uniformly distributed set of numbers between 1 and 10 with a mean of 5.5 and a standard...

Rolling a fair ten dash sided ten-sided die produces a uniformly distributed set of numbers between 1 and 10 with a mean of 5.5 and a standard deviation of 2.872 Assume that n ten dash sided ten-sided dice are rolled many times and the mean of the n outcomes is computed each time.

a. Find the mean and standard deviation of the resulting distribution of sample means for nequals

=144

The mean of the resulting distribution of sample means is .

​(Round to the nearest tenth as​ needed.)

The standard deviation of the distribution of sample means is

​(Round to the nearest thousandth as​ needed.)

b. Find the mean and standard deviation of the resulting distribution of sample means for nequals =81

The mean of the resulting distribution of sample means is .

​(Round to the nearest tenth as​ needed.)

The standard deviation of the distribution of sample means is

​(Round to the nearest thousandth as​ needed.)

c. Why is the standard deviation in part a different from the standard deviation in part​ b? Choose the correct answer below.

A.

With larger sample sizes​ (as in part​ a), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation.

B.

With larger sample sizes​ (as in part​ a), the means tend to be further​ apart, so they have more​ variation, which results in a bigger standard deviation.

C.

With smaller sample sizes​ (as in part​ b), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation.

D.

With smaller sample sizes​ (as in part​ b), the means tend to be further​ apart, so they have more​ variation, which results in a smaller standard deviation.

we are given that σ=2.872 and µ=5.5 The mean of sampling distribution is given by population mean and the standard... View the full answer

• So far so good Im going to be posting quite a few questions, thanks for all the help.
• silentsteel
• Apr 03, 2018 at 7:43pm
• OK. Always happy to help.
• Stat.Solve
• Apr 03, 2018 at 7:48pm
• I have another one I took a picture of it would you want to try that one ?
• silentsteel
• Apr 03, 2018 at 7:51pm
• OK.
• Stat.Solve
• Apr 03, 2018 at 7:58pm

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