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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