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1. There are five people in a room. What it’s the probability that at least two of them were born in the same month? (Assume all birth months are equally likely) P(at least two of them born in same month) = 1 – P(none of them born in same month) = 1 – 12x11x10x9x8 / 125 = 1 – 0.382 = 0.618 2. Bruce is thinking about moving from Gotham City to Metropolis and wonders what will happen to his heating and cooling bill. The only information he has at his disposal is the following table City Gotham Metropolis Mean Daily Temperature (F) 64 64 Standard Deviation for the Daily Temperature (F) 16 5 Based only on this information, do you think Bruce’s heating and cooling costs would be greater in Gotham City or Metropolis? Explain your answer. Mean daily temperature is the same for both cities so Bruce’s heating and cooling costs wouldn’t be different. It is more variable in Gotham city though. 3. The 1999 monthly cost for health care for an employee and two dependents is given in the table Provider Maxicare Cigna Health Net Pacific Care Health Plan of Redwoods Cost $410 $425 $426 $428 Provider Kaiser Aetina Blue Shield HMO Omni Healthcare $434 Lifeguard Cost $436 $436 $447 $458 $458 a. Find the three quartiles for the monthly cost of health care b. Draw a box plot for the monthly cost of health care (ranked from lowest to highest) Q1 = 426 Q2 = 435 Q3 = 447 410 426 435 447 458 4. Suppose that people’s height (in cm) are normally distributed, with a mean of 170 cm and a standard deviation of 5 cm. We find the heights of 50 people. a. How many of these people would you expect to be taller than 168 cm? b. How many of these people would you expect to be taller than 170 cm? c. Find the probability that a randomly selected person in this group is in between 170 and 180cm tall. a. P(x > 168) = P(z > (168-170)/5) = P(z > -0.4) = 0.6554 Number of people = 0.6554(50) = 33 b. P(x > 170) = P(z > (170-170)/5) = P(z > 0) = 0.5 Number of people = 0.5(50) = 25 c. P(170 < x < 180) = P(0 < z < 2) = 0.4773 Number of people = 0.4773(50) = 24