Download Section 5.2 Simulations

Section 5.2 Using Simulation to Estimate Probabilities
Statistics
(Problems from pages 310 – 315 of text)
P10.) How would you use a table of random digits to conduct one run of a
simulation of each situation?
a.) There are eight workers, ages 27, 29, 31, 34, 34, 35, 42, and 47. Three
are to be chosen at random for layoff.
b.) There are 11 workers, ages 27, 29, 31, 34, 34, 35, 42, 42, 42, 46, and 47.
Four are to be chosen at random for layoff.
P11.) Researchers at the Macfarlane Burnet Institute for Medical Research and
Public Health in Melbourne, Australia, noticed that the teaspoons had
disappeared from their tearoom. They purchased new teaspoons, numbered
them, and found that 80% disappeared within 5 months.
Suppose that 80% is the correct probability that a teaspoon will disappear
within 5 months and that this group purchases ten new teaspoons. Estimate
the probability that all the new teaspoons will be gone in 5 months.
Start at the beginning of row 34 of Table D on page 828, and add your ten
results to the frequency table in Display 5.21, which gives the results of
4990 runs.
a.) What are the assumptions that you are making?
b.) Make a table that shows how you are assigning the random digits to the
outcomes. Explain how you will use the digits to model the situation
and what summary statistic you will record.
c.) Repetition. Conduct ten runs of the simulation, using the beginning of
row 34 from Table D on page 828. Add your results to the frequency
table given for Display 5.21 on page 310.
d.) With your 10 results included, what is the probability that all the new
teaspoons will be gone in 5 months?
P12.) A catastrophic accident is one that involves severe skull or spinal damage.
The National Center for Catastrophic Sports Injury Research reports that
over the last 21 years, there have been 101 catastrophic accidents among
female high school and college athletes. Fifty-five of these resulted from
cheerleading.
Suppose you want to study catastrophic accidents in more detail, and you
take a random sample, without replacement, of 8 of these 101 accidents.
Estimate the probability that at least half of your eight sampled accidents
resulted from cheerleading.
Start at the beginning of row 17 of Table D on page 828, and add your ten
runs to the frequency table in Display 5.22, which gives the results of 990
runs.
a.) What are the assumptions that you are making?
b.) Make a table that shows how you are assigning the random digits to the
outcomes. Explain how you will use the digits to model the situation
and what summary statistic you will record.
c.) Repetition. Conduct ten runs of the simulation, using the beginning of
row 17 from Table D on page 828. Add your results to the frequency
table given for Display 5.22 on page 311.
d.) With your 10 results included, what is the probability that at least half
of your eight sampled accidents resulted from cheerleading?
P13.) The winner of the World Series of baseball is the first team to win four
games. That means the series can be over in four games or can go as many
as seven games. Suppose the two teams playing are equally matched.
Estimate the probability that the World Series will go seven games before
there is a winner.
Start at the beginning of row 9 of Table D on page 828, and add your ten
runs to the frequency table in Display 5.23 on page 311, which gives the
results of 4990 runs.
a.) What are the assumptions that you are making?
b.) Make a table that shows how you are assigning the random digits to the
outcomes. Explain how you will use the digits to model the situation
and what summary statistic you will record.
c.) Repetition. Conduct ten runs of the simulation, using the beginning of
row 9 from Table D on page 828. Add your results to the frequency
table given for Display 5.23 on page 311.
d.) With your 10 results included, what is the probability that the World
Series will go seven games before there is a winner?