MAT212 - Activity #6: The Central Limit Theorem (25 points) Directions: For this activity, you will be rolling 4 dice and using your calculator. Let X be a random variable representing the roll of a fair 6-sided die. Complete the following table which will represent the theoretical distribution of X (Value of the Die and its corresponding probability). This represents the distribution of your population, since we are examining the theoretical outcome of QL possible rolls of the die. So, in the table below, state the probability of each number when rolling a six- sided die. Table 1 -Theoretical Probabilities (3 points) 3 1_Now we will conduct our experiment: is Roll your 4 dice and calculate the average of these 4 rolls (5) in the rst box (Trial #1) in Table 2 provided below. b, New repeat the previous step 40 times. You should have 40 )7 written in Table 2. This is your sampling distribution. o. Now sort your 40 values of f and complete Table 3 given below. 2. We will now consu'uct two histograms on the top and bottom of this page: The top histogram will be our population from Table 1 (single roll of a die). The bottom histogram will be our sampling distribution of the sample mean from Table 3 (mean of n=4 rolls of a die). Remember, the horizontal axis represents the possible values of the random variable while the vertical axis represents the probability of getting the particular value. Draw a rectangle with the value in the center of the rectangle. Histogram 1: Theoretical Probabilities (n=1} (2 points) 0-75 0.7\" 0.86 0.66