# 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

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