<< Chapter < Page Chapter >> Page >

It has been stated that about 41% of adult workers have a high school diploma but do not pursue any further education. If 20 adult workers are randomly selected,

  1. find the probability that 12 of them have a high school diploma but do not pursue any further education.
  2. find the probability that at most 12 of them have a high school diploma but do not pursue any further education.
  3. Find how many adult workers do you expect to have a high school diploma but do not pursue any further education.

Let X = the number of workers who have a high school diploma but do not pursue any further education.

X takes on the values 0, 1, 2, ..., 20 where n = 20, p = 0.41, and q = 1 – 0.41 = 0.59. X ~ B (20, 0.41)

  1. P X=12 20 12 0.41 12 0.59 8 0.04173
  2. P ( x ≤ 12) = 0.9738. (calculator or computer)

Using ti-83,83+,84,84+ calculator

Go into 2 nd DISTR. The syntax for the instructions are as follows:

To calculate ( x = value): binompdf( n , p , number) if "number" is left out, the result is the binomial probability table.
To calculate P ( x ≤ value): binomcdf( n , p , number) if "number" is left out, the result is the cumulative binomial probability table.
For this problem: After you are in 2 nd DISTR, arrow down to binomcdf. Press ENTER. Enter 20,0.41,12). The result is P ( x ≤ 12) = 0.9738.

Note

If you want to find P ( x = 12), use the pdf (binompdf). If you want to find P ( x >12), use 1 - binomcdf(20,0.41,12).

The probability that at most 12 workers have a high school diploma but do not pursue any further education is 0.9738.

The graph of X ~ B (20, 0.41) is as follows:

This histogram shows a binomial probability distribution. It is made up of bars that are fairly normally distributed. The x-axis shows values from 0 to 20. The y-axis shows values from 0 to 0.2 in increments of 0.05.

The y -axis contains the probability of X , where X = the number of workers who have only a high school diploma.

c. The number of adult workers that you expect to have a high school diploma but not pursue any further education is the mean, μ = np = (20)(0.41) = 8.2.

The formula for the variance is σ 2 = npq . The standard deviation is σ = n p q .
σ = ( 20 ) ( 0.41 ) ( 0.59 ) = 2.20.

Try it

About 32% of students participate in a community volunteer program outside of school. If 30 students are selected at random,

  1. find the probability that 14 of them participate in a community volunteer program outside of school.
  2. find the probability that at most 14 of them participate in a community volunteer program outside of school. Use the calculator or computer to find the answer.

  1. P X=14 30 14 0.32 14 0.68 16 0.03588
  2. 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 ( 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

Questions & Answers

what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to statistics i - stat 213 - university of calgary - ver2015revb' conversation and receive update notifications?

Ask