







Liza works for a call center 
20191031 

From Timothy: Liza knows that in the long term, she has a 65% chance of making a sale when calling on customers. One morning, he makes Six calls.
a. What is her probability of making three calls?
b. What is her probability of making sales fewer than three? Answered by Penny Nom. 





A binomial probability question 
20191008 

From venni: The Medassist Pharmaceutical Company receives large shipments of aspirin
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 doesn’t
meet the required specifications. If a particular shipment of thousands of
aspirin tablets actually has a 4% rate of defects, what is the probability that
this whole shipment will be accepted? Answered by Penny Nom. 





The binomial distribution 
20191001 

From PY: An online game called ‘Shop Quiz’ is held by an ecommerce platform, from Monday to Friday
every week. It consists of 8 multiple choice questions (MCQ) and each question has four options (A, B, C, D). Only one option is the correct answer. People who are able to correctly answer all 8
questions are winners and will be awarded a number of online shopping credits.
Let X represent the number of questions that a person can answer correctly in a ‘Shop Quiz’.
1) Explain why Binomial distribution might NOT be a suitable distribution for the random variable
X.
Mr. Saul likes playing the quiz, however, he is afraid that he might not have the necessary knowledge to answer the quiz questions. (The quiz questions cover a variety of topics including science, history, entertainment, sports and geography, etc.) Therefore, he tries to win the game by simply guessing the answers to each question. Answered by Penny Nom. 





Sample size 
20100329 

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 
20100227 

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 
20080913 

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 
20080413 

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 
20080327 

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 
20071021 

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 
20070930 

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 
20070901 

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(1p). I understand how to get the np but not understanding how to get the (1p). For example np=(40)(0.48)(10.48)=3.160. How can I get the (10.48) answer please Answered by Harley Weston. 





Find the sample size needed 
20070513 

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 
20070409 

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 
20070329 

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 
20061129 

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 
20061121 

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 
20060520 

From Glenn: What is the correct formula for coefficient of variation for a binomial distribution? Answered by Penny Nom. 





A manufacturer of cotton pins 
20060320 

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 
20060121 

From Belinda: In a survey of 15 manufacturing firms, the number of firms that use LIFO (a lastin firstout 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 
20060121 

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 
20051203 

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? 
20040331 

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 
20031217 

From Lesley: my daughter is having difficulty with the following formula
P(X=x) = ( n over x) px (1p) nx
The teacher has given them the formula but not taught them how to apply it or understand it. Answered by Penny Nom. 





Cinderella clothes 
20011211 

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 
20001103 

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 
20001007 

From A student: If the falsepositive 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 falsepositive result to be at most 0.2? Answered by Harley Weston. 





What is the variance of the difference of two binomials? 
19960208 

From Chris Johnson: My coworkers and I have come up with different estimates of the zstatistic, 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. 

