Stats

The assignment consists of 5 problems. A hard copy (handwritten is fine) of this

assignment is due in class on Wednesday September 3, 2014. Please write your names

(or ids), mailbox number you want it delivered and honor code on the assignment. You

may do the assignment either individually or a group of not more than two people. If you

do the assignment in a pair please make sure that you only submit one assignment.

Show as much working as possible. For example, instead of writing the final probability,

write PDF.BINOM (6, 8, 0.45). There are no Poisson problems in this assignment.

Problem 1

A European car manufacturer is interested in gender differences in car colors. They identify consumers who are loyal to the brand and do a survey of the colors these people like. The results of the survey are given in the table below (You have to read your immersion notes for this one). It is OK to write the results in fractions.

| Gender |

| Male | Female | Total |

Black Preferred | 40 | 10 | 50 |

Silver Preferred | 20 | 60 | 80 |

Total | 60 | 70 | 130 |

(i)What is the probability of selecting a male customer for the survey? (ii) What is the probability that silver is preferred? (iii) What is the probability of selecting a male and someone who prefers black cars? (iv) What is the probability of selecting a male or someone who prefers black cars? (v) Are gender and color preferences independent?

(You can write the answers in fractions).

P(i) Male = 60/130 = 0.4615

P(ii) Silver = 80/130 = 0.6154

P(iii) Male & Black = 40/130 = 0.3077

P(iv) Male or Black = (60/130) + (50/130) – (40/130) = 0.5385

P(v) No, gender and color preferences are dependent.

Problem 2

Your firm has bought large quantities of a new machine. Now you face the decision on whether to purchase an extended service contract that will cover all maintenance expenses. The contract costs $10000 per machine. After gathering several opinions, you...