Question

Assignment Directions

1. Answer the following critical thinking questions in this forum. Feel free to copy the questions and paste into your reply so that you cover each one. Use complete sentences and proper statistical terminology in all posts.
2. Read the instructors response to the questions.
3. Read the answers of some of your peers.
4. Make a reply to your own post with any corrections to your responses.
5. Read the answers of some of your peers and make a reply to at least one other person. Make sure you reply using the standard assessment format (SII - Strength: what is the greatest strength of the person's post; Improvement: how can they improve in future assignments; Insight: something insightful you find out from assessing their performance.) Your goal is to help the student improve their future performance, NOT judge the quality of the post. Check the feedback from your practice self-assessment and use this to guide your peer assessment. If you still have questions about what constitutes an assessment then go to the Course Information folder and view the presentation linked under the heading "Assessment".

Note: This Experience contains a Peer Assessment assignment (see above directions)

Questions:

1. How do you know when to use the binomial distribution to model a situation? What are the requirements for a binomial experiment? [4 bullets]
2. When dealing with the binomial distribution, why are the possible values for the random variable always 0,1,2,3,…,n where n is the number of trials or sample size? Why can't we use negative values, or fractions, or numbers greater than n? [3 sentences]
3. Under what conditions is a binomial distribution symmetric? Skewed left? Skewed right? Why? [3 sentences]
4. How is the area in the bars of a binomial histogram related to the probability of choosing those X values? (Hint: figure it out for a single bar) [3 sentences]

Answer 1

1) The number of observations n is fixed.

2: Each observation is independent.

3: Each observation represents one of two outcomes ("success" or "failure").

4: The probability of "success" p is the same for each outcome.

Since x denotes the number of successes and it cannot be negative hence the random variable x and the number of trials n cannot be negative

1. n, the number of independent trials
2. p, the probability of success

For small p and small n, the binomial distribution is what we call skewed right

For large p and small n, the binomial distribution is what we call skewed left.

For p = 0.5 and large and small n, the binomial distribution is what we call symmetric.

As n increases, the binomial distribution becomes skewed right As n increases, the binomial distribution becomes more bell shaped As n decreases, the binomial distribution becomes more bell shaped D.