Mathematics Question

Assignment One

Design a binomial experiment you would need three things  (You will need StatCrunch to answer the probability question)

• The Trial: it should only have two outcomes, such as “heads or tails”, “would I make it to work on time or not”, or “students who pass or fail Math 227”, etc. Also need to decide how many trials you would do.
• The Theoretical Percentage of Success for each trial: you may not know this, so give me a good, educated guess.
• What’s the probability of “x times” happening?

My example –

The Trial:  Finding a parking spot in Costco Pacoima, right in front of main entrance on a Sunday. I’m going there 5 times. (“Success” means you found a spot right in front of the main entrance.)

The Theoretical Percentage of Success each trial:    20% (that’s my guess of finding a parking spot in front of the main entrance on any given Sunday.)

What’s the percentage of “Success” all 5 times? So, I do 5 trials n = 5 (total trials), p=0.2 (theoretical probability), x = 5 (how many times I want to see it happen). Using StatCrunch by doing Stat, Calculators, Binomial I get the probability is 0.00032 – which means that my chance of finding a spot to park in front of the main entrance on a Sunday all five times is 3/10000. Your example does not have to include the success in all 5 trials (that was just my random pick). You may do less than the total number of trials.

Assignment TwoInstructions:

You can write your work on paper and attached a pdf file (picture or scan) or you can type your solutions here using the text editor. You will need StatCrunch in order to complete this activity.

Traditionally, when students take Ramos’ Math 227 class at Mission College, about 70% of students in his Statistics courses at LAMC are successful. Suppose 25 students are selected at random from all previous students in this course. What is the probability that “more than” 15 of them will have been successful in the course? 

Let’s do a quick overview of the criteria for a binomial experiment to see if this fits.

• A fixed number of trials – ( what are these in our experiment and how many? )
• Each trial is independent of the others – ( are all trials independent and why? ) 
• There are only two outcomes – ( what are the only two outcomes?)
• The probability of each outcome remains constant from trial to trial. – ( what is this probability of success ?)