# 4.3 Binomial distribution  (Page 3/29)

 Page 3 / 29

## Try it

About 32% of students participate in a community volunteer program outside of school. If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school. Use the TI-83+ or TI-84 calculator to find the answer.

P ( x ≤ 14) = 0.9695

In the 2013 Jerry’s Artarama art supplies catalog, there are 560 pages. Eight of the pages feature signature artists. Suppose we randomly sample 100 pages. Let X = the number of pages that feature signature artists.

1. What values does x take on?
2. What is the probability distribution? Find the following probabilities:
1. the probability that two pages feature signature artists
2. the probability that at most six pages feature signature artists
3. the probability that more than three pages feature signature artists.
3. Using the formulas, calculate the (i) mean and (ii) standard deviation.
1. x = 0, 1, 2, 3, 4, 5, 6, 7, 8
2. X ~ B $\left(100,\frac{8}{560}\right)$
1. P ( x = 2) = binompdf $\left(100,\frac{8}{560},2\right)$ = 0.2466
2. P ( x ≤ 6) = binomcdf $\left(100,\frac{8}{560},6\right)$ = 0.9994
3. P ( x >3) = 1 – P ( x ≤ 3) = 1 – binomcdf $\left(100,\frac{8}{560},3\right)$ = 1 – 0.9443 = 0.0557
1. Mean = np = (100) $\left(\frac{8}{560}\right)$ = $\frac{800}{560}$ ≈ 1.4286
2. Standard Deviation = $\sqrt{npq}$ = $\sqrt{\left(100\right)\left(\frac{8}{560}\right)\left(\frac{552}{560}\right)}$ ≈ 1.1867

## Try it

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

1. What is the probability distribution for X ?
2. Use your calculator to find the following probabilities:
1. the probability that 25 adults in the sample prefer saving over spending
2. the probability that at most 20 adults prefer saving
3. the probability that more than 30 adults prefer saving
3. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
1. X B (50, 0.6)
2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
1. P ( x = 25) = binompdf(50, 0.6, 25) = 0.0405
2. P ( x ≤ 20) = binomcdf(50, 0.6, 20) = 0.0034
3. P ( x >30) = 1 - binomcdf(50, 0.6, 30) = 1 – 0.5535 = 0.4465
1. Mean = np = 50(0.6) = 30
2. Standard Deviation = $\sqrt{npq}$ = $\sqrt{50\left(0.6\right)\left(0.4\right)}$ ≈ 3.4641

The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Suppose we randomly sample 200 people. Let X = the number of people who will develop pancreatic cancer.

1. What is the probability distribution for X ?
2. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
3. Use your calculator to find the probability that at most eight people develop pancreatic cancer
4. Is it more likely that five or six people will develop pancreatic cancer? Justify your answer numerically.
1. X B (200, 0.0128)
1. Mean = np = 200(0.0128) = 2.56
2. Standard Deviation =
2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
P ( x ≤ 8) = binomcdf(200, 0.0128, 8) = 0.9988
3. P ( x = 5) = binompdf(200, 0.0128, 5) = 0.0707
P ( x = 6) = binompdf(200, 0.0128, 6) = 0.0298
So P ( x = 5)> P ( x = 6); it is more likely that five people will develop cancer than six.

## Try it

During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the highest field goal completion rate in the league. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points.

1. What is the probability distribution for X ?
2. Using the formulas, calculate the (i) mean and (ii) standard deviation of X .
3. Use your calculator to find the probability that DeAndre scored with 60 of these shots.
4. Find the probability that DeAndre scored with more than 50 of these shots.
1. X ~ B (80, 0.613)
1. Mean = np = 80(0.613) = 49.04
2. Standard Deviation = $\sqrt{npq}=\sqrt{80\left(0.613\right)\left(0.387\right)}\approx 4.3564$
2. Using the TI-83, 83+, 84 calculator with instructions as provided in [link] :
P ( x = 60) = binompdf(80, 0.613, 60) = 0.0036
3. P ( x >50) = 1 – P ( x ≤ 50) = 1 – binomcdf(80, 0.613, 50) = 1 – 0.6282 = 0.3718

where do I start
in a large restaurant an average of every 7 customers ask for water with the their meal. A random sample of 12 customers is selected, find the probability that exactly 6 ask for water with their meal
any body with idea
Rufai
conditional probability
Ramesh
Rufai
iam really sorry. it's been long since I used these things. I just gave you a hint though
Ramesh
ok
Rufai
this follows binomial distribution. p(X=6)=12C6*(0.6)^6*0.4^6 use this formula n find.
syeda
can you explain the cosidered variable in the formula
Divya
x is variable wich is exactly 6 costumers
syeda
n is number of customers
syeda
ncx*p^X*q^X?
Divya
q^n-x
syeda
oh right !!! thanks yaar
Divya
I agree with Seyda too
Hoshyar
I agree with Syeda too
Hoshyar
7/12 =0.58is it?
yousaf
.
yousaf
r8
khalid
what is descriptive statistic
Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread).
Divya
are you getting this ?
Divya
if so let me know
Divya
yes m getting
Ramesh
fine
Divya
what's taking place can l join u
Anest
yeah !!why not? sure
Divya
okey thanks
Anest
where are statistics used
hello
Giannis
Hi
Makhosi
how u doing
Muhid
the upper quartile of the population 10,12,14,16,18,20,25,15,11,11,17,is................?
Gach
The probability range is 0 to 1... but why we take it 0 to 1....
because in probability 1 means success and 0 means failure and it cnnt be more or less than 1 and 0.
syeda
b/c v hv mazimum probibliy 1 and minimum which is.no.probiblity is 0.so.v hv the range from 0 to 1
khalid
the size of a set is greeter than its subset
Hoshyar
The probability of an event will not be less than 0.  This is because 0 is impossible (sure that something will not happen).The probability of an event will not be more than 1. This is because 1 is certain that something will happen
Divya
what do they mean in a question when you are asked to find P40 and P88
Mani
hi
Mehri
you're asked to find page 40 and page 88 on that particular book.
Joseph
hi
ravi
any suggestions for statistics app better than this
ravi
sorry miss wrote the question
omar
No problem) By the way. I NEED a program For statistical data analysis. Any suggestion?
Mani
Eviews will help u
Hello
Okonkwo
arey there any data analyst and working on sas statistical model building
ravi
Hi guys ,actually I have dicovered that the P40 and P88 means finding the 40th and 88th percentiles 😌..
Megrina
who can explain the euclidian distance
ravi
I am fresh student of statistics (BS) plz guide me best app or best website relative to stat topics
Noman
IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are the mean, median, and mode.
define the measures of location
IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are th
Ahmed
hi i have a question....
what is confidence interval estimate and its formula in getting it
discuss the roles of vital and health statistic in the planning of health service of the community
given that the probability of
BITRUS
good morning
Rufai
hi bitrus.
Bratit
hi
yousaf
hallo
Bratit
hey
Divya
uses in health policy and health research
Divya
1) social inequalities I health 2) Trends in mortality
Divya
hey do you know any about any of the statistics courses which is best ?
Divya
hello
Hoshyar
hi
Hoshyar
online courses and convenient fees
Divya
can man city win Liverpool ?
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped. (a) what is probability it lands on heads? (b) given that it lands on tail, what is the Condi
0.5*0.5+0.5*0.6
Ravasz
It should be a Machine learning terms。
Mok
it is a term used in linear regression
Saurav
what are the differences between standard deviation and variancs?
Enhance
what is statistics
statistics is the collection and interpretation of data
Enhance
the science of summarization and description of numerical facts
Enhance
Is the estimation of probability
Zaini
mr. zaini..can u tell me more clearly how to calculated pair t test
Haai
do you have MG Akarwal Statistics' book Zaini?
Enhance
Haai how r u?
Enhance
maybe .... mathematics is the science of simplification and statistics is the interpretation of such values and its implications.
Miguel
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Haai
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Kawuma
Hi. Im raph. Can anyone teach me how to read the z-table?
Asare