Discussion Four I. (9 points) Design a binomial experiment - following these steps Step 1: You need to decide on "the trial": what are you testing? Your trial, whatever it is, should only have two outcomes, such as "coin toss" (heads or tails), "would I make it to work on time or not" (on time, or late), or "Shaq's free throws" (he makes it, or he doesn't make it), etc. Step 2: Decide how many trials you would do in your experiment - for example "I'm going to toss the coin 10 times," or "I'm going to test my going to work on time for the next week - i.e. 5 days," or "Shaq is going up to the line 12 times in that one game." This is your n. Step 3: Determine the Theoretical Percentage of Success for each trial: you may or may not know this. Coin toss we know it's 50-50. Going to work on time - give me a good guess. 80% (or 0.8)? 90% (or 0.9)? Shaq's free throw percentage can be found via google. This is your p. Step 4: "What's the probability of 'x times' happening?" For this experiment, I want an outcome that's cumulative. Cumulative means that there are multiple possibilities. Read on...

• For example, for the coin toss, "Given that it's 50-50 heads and tails, what's the probability that I get AT LEAST 7 heads in 10 tosses?" In other words, what's the probability that I get 7, 8, 9 or 10 heads?
• For the Going to Work On Time experiment, you may ask "What's the probability that I make it to work MORE THAN 3out of 5 times, given that my on time percentage is usually 80%?" ("More than 3" out of 5 times means 4 times or 5 times. But it doesn't include 3.)
• For Shaq's Free Throws, you may ask "What's the probability that Shaq makes LESS THAN 10 out of 12 free throws, given that his free throw percentage is something like 40%?" "Less Than 10" means anywhere from zero to nine, but not 10. However, if you say "10 or less", then it includes from zero to 10. You may also say "Less Than Or Equal to 10" if you want to include from zero to 10.

Now, for the above cumulative scenarios, your x is still 7 for the coin toss, 3 for the Work On Time test, and 10 for the Free Throws. BUT...

• Step 6: Go to the web calculator here: http://stattrek.com/online-calculator/binomial.aspx . Plug in your p in "Probability of success on a trial", your n in "Number of trials", your x in "Number of successes". Then click on the "Calculate" button. AND THEN...
• Step 7:
  • Read the result in "Cumulative probability: P(Xx)" for "AT LEAST 7"
  • Read the result in "Cumulative probability: P(X>x)" for "MORE THAN 3"
  • Read the result in "Cumulative probability: P(X
• - those would be the probability of your Part II binomial experiment, with all the multiple possibilities included.
• Report your answer.

You do not need to calculate the mean or standard deviation for the Part II experiment.

(Note: You must post before seeing other posts.)

III. (8 points) Respond thoughtfully and substantively to another person's post - did they calculate their probabilities correctly? Do you share a similar experience as they do? What would you suggest to improve on their probabilities? (Generic responses that do not specifically addressing the post you are responding to, that I feel you could use to respond to any post will result in zero points.)