In this lab we will have Minitab simulate a number of different situations that can be modeled by binomial distributions.

1. Test time. Just like a bad dream, you find yourself in class faced with taking a 10 question true or false test in which you have no idea at any of the answers. You therefore have to guess. Like most bad dreams, this happens over and over again.  Your task (not part of a bad dream) is to have Minitab "take" this 10 question true or false test 500 times. (To do this go to Calc > Random Data > Binomial. Generate500 rows of data and store these in C1.  The Number of trials should be 10 and the Probability of success should be 0.5.)
1. Make a histogram of your outcomes. In doing so, make the horizontal axis go from 0 to 10.  (To do this, double click on the horizontal axis on your histogram, choose the Binning tab, click on Midpoint, click on Midpoint/cutpoint positions: and type in  0:10/1.)
2. Calculate the sample mean and standard deviation of your data.
3. What is m and s for a binomial distribution where n = 10 and p = 0.5?
4. Your dreams have now gone from bad to worse. You are now faced with a 10 question multiple choice test and each question has 10 answers from which to choose. Repeat questions a through c with this new scenario.  Make sure your histogram again has the horizontal axis go from 0 to 10 in increments of 1.
   

 
2. The Brady Bunch. You and your new spouse are dreaming about your future family of six children. In your mind you are picturing a family similar to the Brady Bunch, three boys and three girls - the youngest one in curls. Your spouse on the other hand is thinking about a family of six strapping young men. (Seven Brides for Seven Brothers is his favorite movie.) You wish to show him that your vision of your future family is more probable than his is. To do this have Minitab "give birth" to 500 families of six children. In doing so, have it count the number of boys in the family. To do this, generate 500 rows of data where there are 6 trials and the probability of success is 0.5.
1. Construct a histogram of your results.
2. What proportion of your simulated families have 3 boys and 3 girls? What proportion of your simulated families have all boys? (To calculate this use Stat > Tables > Tally Individual Variables.)
3. What is the theoretical probability that a family of six has 3 boys and 3 girls? What is the theoretical probability that a family of six has all boys?  (These can be calculated on Minitab under Calc > Probability Distributions > Binomial.  If you do this click on Probability and use the input constant.)

 
3. Is the Sun a Planet?  According to the article, "Contemporary Cosmological Beliefs," that appeared in Social Studies of Science in 1987, 25% of Americans believe that the sun is a planet.  You wonder if 25% of all Holland residents also believe that the sun is a planet.  To find this out, you survey 30 people in Holland to ask them if the sun is a planet.  You find that 6 out of 30 in your sample believe the sun is a planet.  Because this is only 20% of your sample, you wonder if Holland residents have a better understanding of our solar system than all Americans.  You then set out to determine the probability of something as extreme as your results. To do this, have Minitab "survey" 500 samples of 30 Americans each where the probability of success is 25%. Do this by generating 500 rows of data.
1. Construct a histogram of your results.
2. Give the proportion of your samples that contain the numbers that are 6 or less.
3. Find the theoretical probability that 6 or fewer Americans in a sample of 30 believe that the sun is a planet given that 25% of all Americans hold this belief.