Statistics and statistics

Question

Round answers to relative frequency and probability problems to four decimal places. Once again, your answers should be your own and NOT mine.You decide to play a little game.  Someone with a lot a money decides that they will give you $1 each die that comes up to your lucky number.1.  Choose your groups "lucky number" between 1 and 6. 2. Roll three dice 50 times as a group (go to random.org's dice page).  Have one person do this.3. For each roll of the 3 dice, count how many are equal to your lucky number. Have another person keep track of this. a. On how many rolls of the 3 dice did you have 0 of your "lucky" number? b. On how many rolls of the 3 dice did you have exactly 1 of your "lucky" number? c. On how many rolls of the 3 dice did you have exactly 2 of your "lucky" number? d. On how many rolls of the 3 dice did you have all 3 of your "lucky" number? 

HIT SUBMIT after these questions so that the rest may be answered correctly.4. Now figure out your relative frequencies up to four decimal places if necessary. (if something is .5, no need to put .5000). a. What proportion of times did you roll None of your lucky number? b. What proportion of times did you roll exactly 1 of your lucky number? c. What proportion of times did you roll exactly 2 of your lucky number? d. What proportion of times did you roll all 3 of your lucky number? 

5.  Based on your sample above, what is the average number of times your lucky number came up out of 3 (use a weighted average with your values above: use 0,1,2,3 as the values and your frequency as the weight list in your calculator) 6. What is your sample standard deviation (found the same way)? 

Now let's talk about the theoretical distribution (this will be the same for everyone).

7. What is the theoretical probability of one die matching your lucky number?   

8. So  ,      

9. Fill in the Probability Distribution Table Below:

x

P(x)

0

1

2

3

10. Find the theoretical probabilities below:

a. P(x = 3) = 

b. P(0 < x < 3) = 

          c. P(x  2) = 

11.  Now using YOUR SAMPLE, find the relative frequencies of the same events: (These answer will not all be the same)a. Relative frequency (proportion) of times you rolled all lucky numbers = b. Relative frequency of times you rolled more than 0 lucky numbers but less than 3 = c. Relative frequency of times you rolled 2 or more lucky numbers = 12. Thinking about your data vs. theoretical distribution: Do you think your actual outcome fit the data well? Explain why or why not?13. Suppose that the experiment had been repeated 500 instead of just 50 times, which would change?  How would it change?

Answer 1

Lola, this question tells you what to do. Just do it and count to get your data. The rest will follow.