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.

#### Top Answer

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