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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

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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 ( 100 , 8 560 )
    1. P ( x = 2) = binompdf ( 100 , 8 560 , 2 ) = 0.2466
    2. P ( x ≤ 6) = binomcdf ( 100 , 8 560 , 6 ) = 0.9994
    3. P ( x >3) = 1 – P ( x ≤ 3) = 1 – binomcdf ( 100 , 8 560 , 3 ) = 1 – 0.9443 = 0.0557
    1. Mean = np = (100) ( 8 560 ) = 800 560 ≈ 1.4286
    2. Standard Deviation = n p q = ( 100 ) ( 8 560 ) ( 552 560 ) ≈ 1.1867
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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 = n p q = 50 ( 0.6 ) ( 0.4 ) ≈ 3.4641
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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 = n p q  =   (200)(0 .0128)(0.9872) 1. 5897
  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.
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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 = n p q = 80 ( 0.613 ) ( 0.387 ) 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
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Questions & Answers

pls I need understand this statistics very will is giving me problem
Bolanle Reply
Sixty-four third year high school students were given a standardized reading comprehension test. The mean and standard deviation obtained were 52.27 and 8.24, respectively. Is the mean significantly different from the population mean of 50? Use the 5% level of significance.
Daryl Reply
No
Ariel
how do I find the modal class
Bruce Reply
look for the highest occuring number in the class
Kusi
the probability of an event occuring is defined as?
James Reply
The probability of an even occurring is expected event÷ event being cancelled or event occurring / event not occurring
Gokuna
what is simple bar chat
Toyin Reply
Simple Bar Chart is a Diagram which shows the data values in form of horizontal bars. It shows categories along y-axis and values along x-axis. The x-axis displays above the bars and y-axis displays on left of the bars with the bars extending to the right side according to their values.
Muhammad
statistics is percentage only
Moha Reply
the first word is chance for that we use percentages
muhammad
it is not at all that statistics is a percentage only
Shambhavi
I need more examples
Luwam Reply
how to calculate sample needed
Jim Reply
mole of sample/mole ratio or Va Vb
Gokuna
how to I solve for arithmetic mean
Joe Reply
Yeah. for you to say.
James
yes
niharu
how do I solve for arithmetic mean
Joe Reply
please answer these questions
niharu
add all the data and divide by the number of data sets. For example, if test scores were 70, 60, 70, 80 the total is 280 and the total data sets referred to as N is 4. Therfore the mean or arthritmatic average is 70. I hope this helps.
Jim
*Tan A - Tan B = sin(A-B)/CosA CosB ... *2sinQ/Cos 3Q = tan 3Q - tan Q
Ibraheem Reply
standard error of sample
Umar Reply
what is subjective probability
Avela Reply
how to calculate the Steadman rank correlation
David
what is sampling? i want to know about the definition of sampling.
anup Reply
what is sample...?
Abdul Reply
In terms of Statistics or Research , It is a subset of population for measurement.
Da

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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