# 3.5 Tree and venn diagrams  (Page 5/10)

 Page 5 / 10

Suppose that 10,000 U.S. licensed drivers are randomly selected.

1. How many would you expect to be male?
2. Using the table or tree diagram, construct a contingency table of gender versus age group.
3. Using the contingency table, find the probability that out of the age 20–64 group, a randomly selected driver is female.

Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation.

1. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.
2. Assuming that the walkers walk alone, what percent of all commuters travel alone to work?
3. Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?
4. Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?
1. Car, Truck or Van Walk Public Transportation Other Totals
Alone 0.7318
Not Alone 0.1332
Totals 0.8650 0.0390 0.0530 0.0430 1
2. If we assume that all walkers are alone and that none from the other two groups travel alone (which is a big assumption) we have: P (Alone) = 0.7318 + 0.0390 = 0.7708.
3. Make the same assumptions as in (b) we have: (0.7708)(1,000) = 771
4. (0.1332)(1,000) = 133

When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250 spins, 140 showed a head (event H ) while 110 showed a tail (event T ). On that basis, they claimed that it is not a fair coin.

1. Based on the given data, find P ( H ) and P ( T ).
2. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.
3. Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.
4. Use the tree to find the probability of obtaining at least one head.

Use the following information to answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of 3,059 documented cases of AIDS in the county. They were grouped into the following categories:

Homosexual/Bisexual IV Drug User* Heterosexual Contact Other Totals
Female 0 70 136 49 ____
Male 2,146 463 60 135 ____
Totals ____ ____ ____ ____ ____

Suppose a person with AIDS in Santa Clara County is randomly selected.

1. Find P (Person is female).
2. Find P (Person has a risk factor heterosexual contact).
3. Find P (Person is female OR has a risk factor of IV drug user).
4. Find P (Person is female AND has a risk factor of homosexual/bisexual).
5. Find P (Person is male AND has a risk factor of IV drug user).
6. Find P (Person is female GIVEN person got the disease from heterosexual contact).
7. Construct a Venn diagram. Make one group females and the other group heterosexual contact.

The completed contingency table is as follows:

Homosexual/Bisexual IV Drug User* Heterosexual Contact Other Totals
Female 0 70 136 49 255
Male 2,146 463 60 135 2,804
Totals 2,146 533 196 184 3,059
1. $\frac{255}{3059}$
2. $\frac{196}{3059}$
3. $\frac{718}{3059}$
4. 0
5. $\frac{463}{3059}$
6. $\frac{136}{196}$

Answer these questions using probability rules. Do NOT use the contingency table. Three thousand fifty-nine cases of AIDS had been reported in Santa Clara County, CA, through a certain date. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease from heterosexual contact.

1. Find P (Person is female).
2. Find P (Person obtained the disease through heterosexual contact).
3. Find P (Person is female GIVEN person got the disease from heterosexual contact)
4. Construct a Venn diagram representing this situation. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.

conceptual approach to limits
how are limits derived?
lameck
an entire section of calculus is devoted to that explanation.
Pitior
what is statistics?
statistics :- can be defined as the branches of mathematics that deals with the summarizing, analysing,organization and interpretation of data.
Usman
well said
Venkat
can we find Z value on calculator with out using Z table
no
Pitior
why
Maham
can another way is possible ?
Maham
Well you could make a table. And as the function you use the one used at the z table
Luca
The normal function is only one way, so you can only try using different numbers until you get the probability that you have. So that is easier if you have a table
Luca
me don't know nothing about z table and don't know how to see the z value on table can you tell me please how see the value on table
Maham
The z table is the table of the standard normal distribution
Luca
You can look it up on internet, its easier than writing down the normal distribution function (with an integral) and doing a table in the calculator
Luca
OK thanks luca
Maham
yes use pnorm in r
Venkat
pnorm(2.3,mean=0,sd=1)
Venkat
pnorm?
Maham
do u have r software
Venkat
no
Maham
its with tht u will get
Venkat
Venkat
z mathportal calculator
Venkat
calculator
Venkat
OK venkat thanks
Maham
welcome
Venkat
have calculator but don't know how find z value
Maham
ti83
Venkat
hey guys I'm from computer background so what are the concepts I supposed to prepare for interview in statistics
Alwin
descriptive stats
Venkat
inferential stats
Venkat
outlier treatment
Venkat
boxplot
Venkat
ok
Alwin
assumption of linear regression
Venkat
logistic regression
Venkat
k means clustering
Venkat
exact syllabus?
Alwin
type. analytics vidya interview questions statistics
Venkat
listen. data also
Venkat
like this forum
Jameel
My question is "is it only stats?"
Jameel
wer is the problem
Venkat
how find straight line equation in regression
u can find using excel
Venkat
or r studio
Venkat
for regression
Venkat
shall i help
Venkat
im an expert
Venkat
by giving a value to x,y
Ibrokhim
first provide data
Venkat
ill solve and guve
Venkat
ive
Venkat
Maham
maham you posted data
Venkat
Venkat
ok
Maham
x:1,2,3,4,5 y:2,5,6,8,9
Maham
regredsion equation is
Venkat
y=0.9+1.7x
Venkat
reg eq is y=0.9+1.7x
Venkat
slope = 1.7
Venkat
yintercept = 0.9
Venkat
Venkat
thanx venkat naveen😊
Maham
welcome
Venkat
the tenth percentile for land selling at jabi is 35,000 and the nineteenth percentile for the land price in the same area is 225,what is the 10_90 percentile range
what is statistics
statistics is the beach of mathematics which deals with collection ,organisation, presentation, analysis and interpretation of numerical data
Saeed
oh but interpretation of data, like what and how? 🤔
Bhavani
interpretation: Think in a way that you have given a company year turnover and you have a record of 100years and data set is like (Year,Turnover). Now with that data you can interpret many thing how was the company growth, when were the losses and other things
Akash
interpretation: it is a process in which we make a decision about a population on the basis of sample data . example: if we want to interpret the average income of employees for upcoming year so we have to interpret the income of employees on the basis of previous year's income of those employees
Saeed
thank you saeed, Akash. I understood.
Bhavani
how to remember all this formulas easy ly
no easy way
Pitior
best way is to do as many problems as possible
Pitior
Oh
Bhavani
is this the only one room? or separate room for separate users? 🤔
Bhavani
Bhavani
Finding correlation and regression
explain statistics whether it is a science or arts or both
I would say art is a creation. A chef is an artist. They create new dishes just like the painters. I believe one who creates something new, is an artist. So, Statistics is also an art, if you know it, you can create some new formula, theory, law, etcetera. It is also Science. So yes, it is both.
Rohan
how do you use the normal distribution table when testing the hypothesis
Davia
Rohan
percentages of all the possible outcomes are measured. This is so simple and bases on the questionnaire or interview schedule. It's just measuring the probability chances of high %age of the either part of the hypothesis ... dependent ..independent. data is classified on the basis of respondents
saifuddin
how find CV(x) and CV(y) if X: 3,7,5,4,6,9 &Y:4,9,6,4,7,8 please tell
Maham
what percent of the students would be expected to score above 95?
inferential statistics is what?
in which we make infrences (hypothsis)
surpose a data set of 2,3,5,6,1,4 are given find median
lucy
Mean (average) 4... Median (middle term) 3.5.. Mode (frequency) every element in a set has 1 frequrncy
Akash
i arrange the data set in ascending order. that is, 1,2,3,4,5,6. then find the data set that falls in the middle. in this case, 3 & 4 fall in the middle. you then sum and obtain the average. that is, (3+4)/2=3.5. therefore, 3.5 is the median.
Gbenga
both of you are correct.
Joseph
hello guys
Abasikponke
thanks
lucy
great to be here
King
how does a line graph look
King
hi
Davia
hello
lucy
pls who knows how line graph look like
King
line graph usually have a straight line running through axis
Dike
am new here anyone willing to orient me?
Timothy
find the media of the following numbers 61,64,67,70,73
my body pls
lucy
67
Benmike
Benmike
what is the percentile for the set of data in the class C and frequency F(c,f)given by (9.3-9.7,2) (9.8-10.2,5) (10.3-10.7,12) (10.8-11.2,17) (11.3-11.7,14) (11.8-12.2,6) (12.3-12.7,3) (12.8-13.2,1)
how to find median
arrange ascending and desending order than the mid value is Median
rajendra
ok
Hrishe
what if it is a group data
Oloyede
mean/ medium/ mode
Michelle
n\2 and n+1\2
An operational manager at a manufacturing company is interested in the level of satisfaction of computer buyers. The manager has developed a satisfaction scale of 1-10 to mark their level of understanding with the company.What is the population of the interest?
Any clues
Virtual