# statistics

It is known that 60% of people do not respond to mailed questionnaires. In a sample of 20 questionnaires mailed, what is the probability that more than 12 people will respond?

1. 👍 0
2. 👎 0
3. 👁 125
1. probability that 13 respond
p(13)= C(20,13) (.4^13) (.6^7)
= 77520 * 6.71 * 10^-6 * 2.8 * 10^-2
= 1.46 * 10^-2
and for 14
p(14) = C(20,14)(.4^14)(.6^6)
38760 * 2.68 * 10^-6 * 4.67 *10^-2
=.485 * 10^-2
etc for binomial distribution
p(15) = 15504 * .4^15 * .6^5
= .129 * 10^-2
p(16) = 4845 *.4^16 *.6^4
= .027 *10^-2
p(17) = 1140 * .4^17 * .6^3
=.0042 *10^-2
p(18) = 190 * .4^18 * .6*2
=.00047 *10^-2
forget p(19) and p(20), getting too small
2.1*10^-2 = .02

1. 👍 0
2. 👎 0
posted by Damon
2. By the way, n = 20 is high enough so we could use the continuous version, the normal distribution, to approximate and see if we are way off base.
mean no response = 20 * .6 = 12
sigma = sqrt (20*.6*.4) = 2.2
To get more than 12 responding on the continuous distribution we want to be between 12 and 13 responding or between 7 and 8 not responding, call it 7.5
(7.5-12)/2.2 = -2 sigmas from mean
which is .023 in table of F(z) versus z on normal function table.

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### STATISTICS

True or False? A researcher is interested in studying whether there is a correlation of IQ with health. For this purpose he selected a sample of 261 people and asked them to complete two questionnaires: one for IQ and one for

asked by Marian on September 6, 2013
2. ### stat

A MAIL-ORDER FIRM HAS A CIRCULAR WHICH ELICITS A 10 % RESPONSE RATE. SUPPOSE 20 OF THE CIRCULARS ARE MAILED AS A MARKET TEST IN A NEW GEOGRAPHIC AREA. ASSUMING THAT THE 10% RESPONSE RATE IS APPLICABLE IN THE NEW AREA, DETERMINE

asked by siddhi on May 1, 2012
3. ### Statistics

From: Siegel, A.F. (1997). Practical Business Statistics, 3rd Edition. Irwin/McGrawHill. Case - Can This Survey Be Saved? "What's troubling me is that you can't just pick a new random sample just because somebody didn't like the

asked by didier barreto on November 20, 2009
4. ### Statistics

Case - Can This Survey Be Saved? "What's troubling me is that you can't just pick a new random sample just because somebody didn't like the results of the first survey. Please tell me more about what's been done." Your voice is

asked by didier barreto on November 20, 2009
5. ### Statistics

From: Siegel, A.F. (1997). Practical Business Statistics, 3rd Edition. Irwin/McGrawHill. Case - Can This Survey Be Saved? "What's troubling me is that you can't just pick a new random sample just because somebody didn't like the

asked by didier barreto on November 20, 2009
6. ### Math

In 2001, credit card companies mailed 5 billion credit card applications to 262 million people. On average, how many applications were mailed to each person? Express your answer to the nearest whole application.

asked by Noah on November 30, 2009
7. ### math

A book club offer was mailed to a sample of 400 famles. Of these, 80 families ordered books. Next month, the book club offer will be mailed to 20,000 families. What is the predicted number of orders expected from the mailing next

asked by john on September 14, 2011
8. ### statistics

Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a

asked by mary on June 9, 2013
9. ### statistics

Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a

asked by mary on June 9, 2013
10. ### Stats Help!

You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. Upon analyzing the results, you find that the

asked by slomomo on December 2, 2015

More Similar Questions