Download Lab E - College of Science | Oregon State University

Math 245 Lab E
sec 7.1-7.6
Recitation time: ___
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1. A state lottery draws winning numbers every week. Six different numbers are randomly drawn
from the numbers 1 through 50. A player selects six different numbers and pays $1.00 for a ticket.
If the player’s six numbers match the six drawn by the state (in any order) then the player receives
the jackpot or shares it equally with any other winners. For the following questions you may
assume a winner is the sole winner that week.
a) How many different combinations of six numbers are possible?
b) What is the probability of selecting the winning number?
c) If the jackpot is $1 million, find the expected value of a ticket.
d) Ray buys a ticket only if the expected value is $1.00 or more. How large must the jackpot be in
order for Ray to buy a ticket?
2. If no one wins, the jackpot increases. After a sequence of drawings with no winners, suppose the
jackpot increased to $57 million.
a) Find the expected value of a ticket with this new jackpot.
b) A company decides to buy a ticket for every possible combination of numbers so that they are
assured to win the lottery. How many tickets do they need to buy?
c) If the company buys all the tickets as described they will win the lottery, but will they make a
profit? Explain.
3. Suppose Brian makes 65% of his free throws.
a) Find the probability that he makes 3 out of 5 free throws.
b) Find the probability that he makes at least 3 out of 5 free throws.
4. It is estimated that a certain brand of automobile tire has a 0.8 probability of lasting 25,000 miles.
Out of 4 such tires put on a car, find the probability that at least one will have to be replaced before
25,000 miles.
5. Knowing the measures of central tendency (mean, median, mode) and the measures of dispersion
(range, standard deviation) of a data set gives us a more complete view of the nature of the data.
The following situations give only a single measure (the mean). Discuss how your view of the
situation might change if you also knew the size of the standard deviation. Be creative. Explain the
situation with a small standard deviation and then with a large standard deviation.
a. The mean monthly rainfall in Waco, Texas is 2.51 inches.
* with a small standard deviation
* with a large standard deviation
b. The average grade on the test last week was 82%.
* with a small standard deviation
* with a large standard deviation
c. “But, officer, I was averaging 50 miles per hour.”
* with a small standard deviation
* with a large standard deviation
6. Finding the standard deviation of a data set requires a lot of calculations, and the larger the data
set is the longer this will take you and the more chances you have to make a mistake in your
calculations. For this reason, people dealing with large data sets use calculators or computers to
find the standard deviation (as well as other measures). In this problem you get a chance to practice
using the statistics capabilities of your calculator.
The table below gives the population of each Oregon county, as determined by the 2000 census.
County
Baker
Benton
Clackamas
Clatsop
Columbia
Coos
Crook
Curry
Deschutes
Douglas
Gilliam
Grant
Harney
Hood River
Jackson
Jefferson
Josephine
Klamath
Lake
Lane
Lincoln
Linn
Malheur
Marion
Morrow
Multnomah
Polk
Sherman
Tillamook
Umatilla
Union
Wallowa
Wasco
Washington
Wheeler
Yamhill
Population
16,741
78,153
338,391
35,630
43,560
62,788
19,184
21,137
115,367
100,399
1,915
7,935
7,609
20,411
181,273
19,009
75,726
63,775
7,422
322,977
44,479
103,069
31,615
284,838
10,995
660,486
62,380
1,934
24,262
70,548
24,530
7,226
23,791
445,342
1,547
84,992
a. What was the mean population of an Oregon county
in 2000?
b. Explain what your answer to part a tells you.
c. What was the standard deviation of the county
populations in 2000?
d. Explain what your answer to part c tells you.
e. How many counties had populations close to the
mean? (You will have to decide what is “close”, and
explain your decision.)