Statistics
Thursday, May 03, 2012
Today's Agenda:
1. Collect HW #1: Activities 11­7 & 11­8
2. Finish vocabulary from yesterday (if not already done)
3. Activity 11­2 (f ­ h): Random Babies continued
4. Activity 11­10 (modified): Committee Assignments
5. HW #2: Activity 11­6 & 11­9
VOCABULARY
simulation = an artificial representation of a random process used to study the properties of the process long­term
probability = the proportion of a given event compared to the number of trials; how likely the event is to happen
relative frequency = the long­term proportion of an event occurring
empirical estimate = the probability of an outcome based on experimental data
VOCABULARY
equally likely events = events that have the same likelihood of occurring
sample space = an organized list of all possible outcomes
probability distribution = a table that lists all possible "successes" and their respective proportions
expected value = the "average" or predicted outcome
Activity 11­2: Random Babies (continued… again)
(f)
From yesterday’s class results (Block 8), we came up with these empirical probabilities:
Use these empirical probabilities (proportions) to calculate the average number of matches. HINT: Multiply each “count” by the number of matches, add up all of those products and divide by the total number of trials.
(g)
From yesterday’s sample space, we came up with these theoretical probabilities:
Use these theoretical probabilities (proportions) to calculate the expected value.
How do the average in part (f) and the expected value in part (g) compare?
(h)
What is the probability that the result of this random process equals this expected value? Would you say that you “expect” this outcome to occur most of the time? Why or why not?
Activity 11­10: Committee Assignments
(a) Suppose the six committee members are named: Alice, Bonnie, Carlos, Danny, Evan, & Frank.
Describe how you might use a fair, six­sided die to simulate the random selection of two people to be officers for this committee. (HINT: Keep in mind the officers have to be DIFFERENT people.)
Assign a different number to each person then roll the die
twice to see who will be on the committee. If you get the
same number for the second person, roll again so you have
two different people.
If a number is duplicated, skip that pair... go to the next pair.
(b) Use your calculator to carry out this simulation for a total of 50 repetitions (to get 50 pairs of officers). Record how many women were in each pair of officers:
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(c)
Use the following table to calculate the empirical estimates for women:
(d)
Calculate the average number of women in these 50 simulated pairs of officers.
(e)
Use the following table to calculate the empirical estimates for men:
(f)
Calculate the average number of men in these 50 simulated pairs of officers.
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(g)
Create a sample space for the officers (list all possible combinations of two people who could serve as officers… remember that a combination like Alice and Frank is the same pair as Frank and Alice.)
(c)
Use the following table to calculate the theoretical probabilities for women:
(d)
Calculate the expected value for women.
(e)
Use the following table to calculate the theoretical probabilities for men:
(f)
Calculate the expected value for men.