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binomial distribution

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Sample size 2010-03-29
From Rae:
What sample size was needed to obtain an error range of 2% if the following statement was made? "75% of the workers support the proposed benefit package. These results are considered accurate to within + or - 2%, 18 out of 20 times. This seems like a straight forward question but I'm getting it wrong. Could you please help me out even just the set up would be appreciated so I can see if that's where I'm going wrong. Thanks
Answered by Harley Weston.
The binomial distribution 2010-02-27
From Jessica:
A small mobile phone retailer has found that one of their phones has a 12% probability of being faulty and a replacement having to be provided for the customer. They have just received a trial order for 10 phones from their biggest customer who will take their business elsewhere if 20% or more items are faulty.

i) what is the probability that they will lose their biggest customer?

Answered by Penny Nom.
A multiple choice exam 2008-09-13
From Phalange:
A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing.

Answered by Harley Weston.
A coin is tossed 30 times 2008-04-13
From seulki:
coin tossed 30 times, what is the probability that the heads show up fewer than 17 times?
Answered by Harley Weston.
Probability and Merta trains 2008-03-27
From Lorie:
4. Merta claims that 74% of its trains are on time.

a. Find the probability that among the 60 trains, 38 or fewer arrived on time.

Answered by Harley Weston.
A multiple choice exam 2007-10-21
From jon:
a student is taking a multiple choice exam in which each question has four choices. assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C, D) into a box. she randomly selects one ball for each question and replaced the ball in the box. the marking will determine her answer to the question. there are five multiple choice questions on the exam. what's the probability that she will ...
Answered by Stephen La Rocque and Harley Weston.
The normal approximation to the binomial 2007-09-30
From m.j.:
Slot Machines The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution.
Answered by Harley Weston.
Standard deviation 2007-09-01
From Pat:
I have looked over your math question and mines is not there. for a binomiial distribution with parmeter n and p, the mean is np and the standard deviation is np(1-p). I understand how to get the np but not understanding how to get the (1-p). For example np=(40)(0.48)(1-0.48)=3.160. How can I get the (1-0.48) answer please
Answered by Harley Weston.
Find the sample size needed 2007-05-13
From Mini:
Find the sample size needed to be 98% confident thata marketing survey on the proportion of shoppers who use the internet for holiday shopping is accurate within a margin of error of 0.02. Assume that the conditions for a binomial distribution are met, and that a current estimate for a sample proportion does not exist.
Answered by Penny Nom.
A hypothesis test 2007-04-09
From Katrina:
I have already tried to do this problem but im having a very had time with it. Can you please help me.

Glamour Magazine sponsored a survey of 2500 prospective brides and found that 60% of them spent less than $750 on their wedding gown. Use a 0.01 significance level to test the claim that less than 62% of brides spend less than $750 on their wedding gown. How are the results affected if it is learned that the responses were obtained from magazine readers who decided to respond to the survey through an Internet Web site?

Answered by Penny Nom.
Acceptance sampling 2007-03-29
From Katrina:
The Medassist Pharmaceutical Company recieves large shipments of asprin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is only one or none that doesnt meet the required specifications. If a particular shipment of thousands of asprin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?
Answered by Penny Nom.
What is the expected number of ripe and ready to eat watermelons 2006-11-29
From James:
An agricultural cooperative claims 95 percent of the watermelons shipped out are ripe and ready to eat. If 20 watermelons are shipped out , what is the probability that the number of watermelon that are ripe and ready to is (i) exactly 14 (ii) more than 18 (iii) of the 20 watermelons that are shipped what is the expected number of ripe and ready to eat watermelons
Answered by Penny Nom.
Sally plays roulette 2006-11-21
From Sherry:
Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time
Answered by Penny Nom.
The coefficient of variation 2006-05-20
From Glenn:
What is the correct formula for coefficient of variation for a binomial distribution?
Answered by Penny Nom.
A manufacturer of cotton pins 2006-03-20
From Nirmal:
A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity?
Answered by Penny Nom.
A binomial distribution exercise 2006-01-21
From Belinda:
In a survey of 15 manufacturing firms, the number of firms that use LIFO (a last-in first-out accounting procedure for inventory) is a binomial random variable x with n=15 and p=0.2. a) What is the probability that five or fewer firms will be found to use LIFO? Is it unlikely that more than 10 firms will be found to use LIFO? Comment.
Answered by Penny Nom.
A confidence interval 2006-01-21
From Jonathan:

I am attempting to calculate how my confidence interval will widen at the 95% confidence level if my response universe increases from 100 to 150 or to 200.

There is a universe of 54,000. I take a 5% sample for a test universe of 2,700

If my "yes" universe is 100, at the 95% confidence level, what is my +/- range? (i.e +/- 3? +/-5?)

Historically, 6.6% of the 2,700 you say "yes". I am trying to determine how the confidence interval would change if the number of "yes" responders increased to 150 or to 200.


Answered by Penny Nom.
A sample size estimation 2005-12-03
From Ivonne:
I have to do a research about the behavior of library users. We are going to apply a survey to a population of 1280 students (Management an Economics students) but of course we have to do it to a sample....I need to know the size of my sample.
Answered by Penny Nom.
Replacement times for TV sets? 2004-03-31
From Barb:
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e
Answered by Andrei Volodin and Penny Nom.
Binomial distribution 2003-12-17
From Lesley:
my daughter is having difficulty with the following formula P(X=x) = ( n over x) px (1-p) n-x
The teacher has given them the formula but not taught them how to apply it or understand it.

Answered by Penny Nom.
Cinderella clothes 2001-12-11
From A student:
If cinderella clothes, inc. has determined that 0.5% of all incoming phone calls involve complaints, what is the probability that in 200 incoming calls there are more than one complaint?
Answered by Andrei Volodin.
Banana yogurt 2000-11-03
From James:
A grocery store has 100 cartons of banana yogurt in stock.Each carton contains 12 cup of banana yogurts.The probability that a cup has fewer than 20 banana chunks in it is 10 %. So,What is the probability that between 15 and 25 (inclusive) cartons out of the 100 cartons have exactly 3 cups with fewer than 20 banana chunks?
Answered by Harley Weston.
Independent tests 2000-10-07
From A student:
If the false-positive rate of each test in a battery of tests is 0.05, how many independent tests can be included in the battery if we want the probability of obtaining at least one false-positive result to be at most 0.2?
Answered by Harley Weston.
What is the variance of the difference of two binomials? 1996-02-08
From Chris Johnson:
My co-workers and I have come up with different estimates of the z-statistic, and are in particular disagreement over the calculation of Variance for this problem. I am trying to find out, with a five percent level of significance, whether the new form yields a higher rate of return than the old form. Any thoughts, comments, or solutions?
Answered by Harley Weston.
 
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