Activity 3

Activity 3—MATH 250Elements of Statistics Spring 2023
DUE DATE: 02/08/2023
General Instructions: Make sure to save this Excel file often using the filename “yourname Activity3”. Plea
then complete the following questions. NOTE: Read the entire document below to get a feel for the activity
complete, submit your answers to this activity by attaching your Excel file through the completion link in the
assignment description in Blackboard. Use the area to the near right in this Excel worksheet when calculating
collect from the Internet.
Read the Overview before attempting problems 1 and 2
Overview:
If a quarter is a fair coin, then when flipping that coin you would expect the number of heads to be roughly
tosses. That is, you have a theoretical probability of ½ for a head. If you suspected a coin was slightly “to
how would you compute the probability of a head? I expect that you would toss the coin lots of times colle
of number of heads during your many tosses in order to determine the probability of getting heads on this
develop theoretical probabilities when possible, we cannot always know or be able to determine all probab
focus of discussion in the text.)
Use of empirically gathered data is how probabilities are often estimated for events that may be far too com
theoretically or at times to test the validity of a theoretical probability. For example, the National Center for
the center for Disease Control with web site at the link out to the right ) collects and publishes data of a he
contains various types of health data, most of which has already been statistically summarized and stated
“FastStats” found within the “Topics” folder tab on this main page. This FastStat option provides quick ac
interesting health and other issues that are statistically analyzed.
As an example, through use of the CDC Wonder website “Cancer Statistics” link one can search the webs
https://wonder.cdc.gov/cancer.html and can request a Cancer Incidence report for the year 2018, showing
incidences for that year, as well as a breakdown of the types of cancers diagnosed that year. The report s
1,708,921 cancers cases diagnosed that year. Using the U.S. Census website it can be found that the po
2018 was 327,044,416.
Since empirical probability, also known as experimental probability, refers to a probability that is based on
likelihood of an event occurring in the future based on historical data. We can use the probability calculate
number of cancer diagnoses in 2023. To find the number of estimated cancer cases in 2023, we will exte
estimated US population in 2023 will be 339,665,000, calculate the estimate the number of cancer diagnos
table at the right.
A portion of this activity is designed to have you find reliable data from the Internet to estimate probabilities
answer the questions below, feel free to use your own choice of site(s) but do evaluate the site regarding t
provides and only use sites that can be reasonably deemed dependable.
Now, complete the following four problems.
NOTE: To provide proper credit, this activity is based on a document published by Addison Wesley at
http://occawlonline.pearsoned.com/bookbind/pubbooks/triola_awl/chapter2/essay1/
1. a. Using an appropriate and reliable web site with one year’s data from within the last 5 years, research an
of the problem, like the one shown in the example above, that shows the number of cases, the total po
relative frequency (probability). Your table will estimate the probability that a randomly selected person in
pertussis (whooping cough)–not die from the disease, just be afflicted. Be sure to include column head
b. To assist health care providers in the U.S. in medically and financially preparing for whooping cough ca
probability to predict the number of cases in the U.S. in 2023. To do this, extend your table to the right of t
probability calculated in part 1 and the fact that the U.S. population in 2023 is estimated to be 339,665,000
of U.S. whooping cough cases in 2023. Show all work in your table at the right.
c. In the answer box below do these things:
1. Give the emperical probability in a complete sentence.
2. Give the relevant URL(s) you visited to find the information/data.
3. Summarize in a sentence the result of your calculation from part 2 above.
2. a. Using data from any ONE year of your choice in the last 10 years, determine an empirical value that rep
randomly chosen newborn baby in the U.S. will be female. Locate the necessary data on the internet from
relevant URLs along with your answer. (NOTE: We want an empirical probability—don’t assume that ther
newborns being female.) Create a table, like you did for problem #1, to the right of this problem. Sh
would encourage use of CDC’s “WONDER” online database search engine using the topic of natality to fin
b. Next, to assist the long-range plans of advertisement agencies, use your estimated probability value to
U.S. births that will occur in 2023 (assume that the total number of births in 2023 is estimated to be around
spreadsheet at the right, extend your table to show calculations and work needed to produce your predicte
c. Type a summary sentence in the box below intepreting your finding.
Probability Practice
3. Calculate the correct probability based on the given information.
a. Becky is allergic to peanuts. At a large dinner party one evening, she notices that the chees
table contain the following flavors: 8 slices of dark chocolate, 15 slices of caramel, 9 slices o
12 slices of strawberry. Assume the desserts are served to guests at random.
i. What is the probability that the cheesecake served to Becky contains peanuts?
ii. What is the probability that Becky’s dessert does not contain chocolate?
b. A bag of coins has 18 quarters, 32 dimes 15 nickels and 42 pennies. If you randomly draw a
what is the probability that you will obtain:
i. a quarter?
ii. a penny?
iii. either a quarter or a penny?
4. Data was collected and formed the table to the right in reference to the ages and activities chosen by each
different participants at a summer camp. As an aide, first find each column and row total for the tworight. Then, answer the following questions.
a. Suppose that one of the participants from this group is randomly selected. What is the proba
14 years old.
b. Suppose that one of the participants is randomly selected. What is the probability that the ca
swimming?
c. Suppose that one of the participants is randomly selected. What is the probability of selecting
not choose hiking?
d. Suppose that one of the participants is randomly selected. What is the probability that the pa
Under AND chose rappelling?
e. Suppose that one of the participants is randomly selected. What is the probability that the pa
OR chose swimming.
f. Find P (chose hiking | over 14 years old)—probability of chose hiking given the participant is
g. Are the events “participant is Over 14” and “participant chose rappelling” mutually exclusive?
NAME:
name “yourname Activity3″. Please place your name above,
elow to get a feel for the activity before continuing. Once
rough the completion link in the Unit 1 Activity 3
Excel worksheet when calculating values from numbers you
problems 1 and 2!
the number of heads to be roughly half the total number of
ou suspected a coin was slightly “top” heavy and hence unfair,
ould toss the coin lots of times collecting the “empirical evidence”
probability of getting heads on this coin. Although we prefer to
w or be able to determine all probabilities theoretically (the main
ed for events that may be far too complicated to analyze
or example, the National Center for Health Statistics (a division of http://www.cdc.gov/nchs
collects and publishes data of a health related nature. This site
statistically summarized and stated in small “factoids.” Notice the
is FastStat option provides quick access to a large number of
istics” link one can search the website
ce report for the year 2018, showing the total number of cancer
s diagnosed that year. The report shows that there were
website it can be found that the population of the United States in
ers to a probability that is based on historical data, it illustrates the
We can use the probability calculated from 2018 to estimate the
d cancer cases in 2023, we will extend our table, and knowing the
imate the number of cancer diagnoses in 2023. See extended
the Internet to estimate probabilities of certain events. As you
but do evaluate the site regarding the dependability of data it
le.
Cases in 2018
1,708,921
US Population in 2018
327,044,416
Probability
0.00522535
Extended Table:
Cases in 2018
US Population in 2018
1,708,921
327,044,416
Est. Cases in 2023
Est. US Pop. in 2023
1,774,868
339,665,000
Probability
0.00522535
Probability
0.00522535
Your tables for problems 1 and 2 will look like the
extended table illustrated above. Follow this pattern.
Click on the table’s cells if you need help seeing the
calculations.
son Wesley at
m within the last 5 years, research and make a table to the right
ws the number of cases, the total population for that year, and the
that a randomly selected person in the U.S. will be afflicted with
Be sure to include column headings.
lly preparing for whooping cough cases, use your estimated
his, extend your table to the right of this problem, and use the
2023 is estimated to be 339,665,000 people, to predict the number
the right.
data.
m part 2 above.
determine an empirical value that represents the probability that a
necessary data on the internet from a reliable site and submit the
l probability—don’t assume that there is a 50-50 chance of
1, to the right of this problem. Show all calculations. (Hint-ngine using the topic of natality to find appropriate data.)
e your estimated probability value to predict the number of female
hs in 2023 is estimated to be around 3,450,000.) Use cell(s) in the
ork needed to produce your predicted number of females in 2023.
.
Your tables for problems 1 and 2 will look like the
extended table illustrated above. Follow this pattern.
Click on the table’s cells if you need help seeing the
calculations.
evening, she notices that the cheesecake options on the dessert
olate, 15 slices of caramel, 9 slices of chocolate peanut butter, and
to guests at random.
served to Becky contains peanuts?
does not contain chocolate?
42 pennies. If you randomly draw a single coin out of the bag,
e ages and activities chosen by each individual from a group of 200
column and row total for the two-way table of counts at the
ndomly selected. What is the probability that the participant is over
d. What is the probability that the camp participant chose
d. What is the probability of selecting a camp participant that did
d. What is the probability that the participant is 14 years old and
Ages and Activites Chosen by some
Participants at a Summer Camp
Age
Swimming
14 and Under
48
Over 14
24
d. What is the probability that the participant is over 14 years old
hose hiking given the participant is over 14 years old.
hose rappelling” mutually exclusive? Explain.
Always start your table with the known historical data and use it to
calculate the empirical probability.
The yellow highlighted cart uses the historical information given in
the problem. (Same as above.)
1. Cell O41: Notice that the probability is the probaility calculated
from the historical data, so use a cell reference to O39.
2. Cell N41: Use given estimate for total population in 2023. If
this number is not given, research it at a reliable site.
3. Cell M41: This value will be calculated using the probabilty in
O41 and the estimated total population in N41. The calculation is
an estimate because the values in the calculations are estimates.
Activites Chosen by some
ants at a Summer Camp
Hiking
24
38
Rappelling
30
36