Answer:
C) a sample distribution of a sample mean with n = 10
and
Step-by-step explanation:
Here, the random experiment is rolling 10, 6 faced (with faces numbered from 1 to 6) fair dice and recording the average of the numbers which comes up and the experiment is repeated 20 times.So, here sample size, n = 20 .
Let,
= The number which comes up on the ith die on the jth trial.
∀ i = 1(1)10 and j = 1(1)20
Then,
=
= 3.5 ∀ i = 1(1)10 and j = 1(1)20
and,
=
=
=
15.166667
so, =
= 2.91667
and =
Now we get that,
We get that are iid RV's ∀ j = 1(1)20
Let,
So, we get that
= for any i = 1(1)10
= 3.5
and,
Hence, the option which best describes the distribution being simulated is given by,
C) a sample distribution of a sample mean with n = 10
and