## Probability And Statistics

Exercise 1
(Use Excel or Minitab or SPSS for this exercise)
The following is a sample of nine mortgage companies’ interest rates for 30-year home mortgages, assuming 5% down.
7.625 7.500 6.625 7.625 6.625 6.875 7.375 5.375 7.500
(a) Find the mean and standard deviation and interpret.
(b) Find lower and upper quartiles, median, and interquartile range. Check for any outliers and interpret.
Exercise 2
If the probability that an individual suffers an adverse reaction from a particular drug is known to be 0.001, determine the probability that out of 2000 individuals,
(a) exactly three and (b) more than two individuals will suffer an adverse reaction.
Exercise 3
In a certain pediatric population, systolic blood pressure is normally distributed with mean 115 mm Hg and standard deviation 10 mm Hg. Find the probability that a randomly selected child from this population will have:
(a) A systolic pressure greater than 125 mm Hg.
(b) A systolic pressure less than 95 mm Hg.
Exercise 4
The following is a random sample of height (in inches) and weight (in pounds) of seven basketball players.
Height 73 83 77 80 85 71 80
Weight 186 234 208 237 265 190 220
Calculate the least-squares regression line for these data using Excel, Minitab or SPSS.

## For this module’s assignment review the following. Voting Theory A group of stud

For this module’s assignment review the following.
Voting Theory
A group of students were asked to vote on their favorite horror films. The candidate films are: Abraham Lincoln Vampire Hunter, The Babadook, Cabin Fever, and Dead Snow (A, B, C, D for short). The following table gives the preference schedule for the election.
How many students voted? How many first place votes are needed for a majority?
Use the plurality method to find the winner of the election.
Use the Borda count method to find the winner of the election.
Use the plurality-with-elimination method to find the winner of the election.
Use the pairwise-comparisons method to find the winner of the election.
Sharing by Value
Cake Sharing by Value
Three players (April, Brandy and Cindy) are sharing a cake. Suppose that the cake is divided into three slices (s1, s2, s3). The following table gives the value of each slice in the eyes of each of the players. (A fair share would be 1/3 = 0.333 = 33.3% or greater.)
Which of the three slices are fair shares to April?
Which of the three slices are fair shares to Brandy?
Which of the three slices are fair shares to Cindy?
Find a fair division of cake using S1, S2, and S3 as fair shares. If this is not possible, explain why not.
Sharing by Percentage
Cake Sharing by Percentage
Three players (Adam, Bob and Chad) are sharing a cake. Suppose that the cake is divided into three slices (s1, s2, s3). The percentages represent the value of the slice as a percent of the value of the entire cake. (A fair share would be 1/3 = 0.333 = 33.3% or greater.)
Which of the three slices are fair shares to Adam?
Which of the three slices are fair shares to Bob?
Which of the three slices are fair shares to Chad?
Find the fair division of the cake, using s1, s2 and s3 as fair shares. If this is not possible, explain why not.
Submit your answers to the questions above by downloading and completing the Voting Theory and Game Theory Worksheet below.

## This is a question about “Newcomb’s Problem”. Two boxes, one transparent and vis

This is a question about “Newcomb’s Problem”.
Two boxes, one transparent and visibly containing \$1,000 (A), and one opaque (B) are placed before an agent X at time t.  The contents of A are supposed fixed, the contents of B known by the agent to have been determined by the prior action of a highly accurate Predictor that has placed \$1,000,000 in box B if it predicted that X will select only box B and has placed nothing in box B if it predicted that X will select both boxes.
A)Assume (for the sake of argument) a universal acceptance of the in fact  completely discredited hypothesis that the strong statistical correlation between smoking and a host of serious diseases including lung cancer is accounted for by a genetic factor that is the common cause of both.  In your view, can someone who believes that these statistics should not in themselves present a deterrent to smoking reconcile this view with an advocacy of the “one-box” solution to Newcomb’s Problem?
B)Suppose that the back of box B is transparent, and that a completely trustworthy and reliable friend of X is able to see whether \$1,000,000 is in box B.  Assume that the Predictor can predict what if anything the friend will say and what X will hear, and that it has factored this into its prior analysis and decision.  If the friend were able to communicate with X, does it matter whether i)the friend simply recommends a selection (“Take both boxes!”) or ii)reveals the actual contents of box B to X (e.g., “Box B is empty”)?  Why or why not?  If the friend were able to announce out loud the contents of box B, would it be advantageous for X to place himself in a situation in which he is unable to make out what his friend says?  Explain.