







Continuity on a closed interval 
20140921 

From Pragya: The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval,
but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's
limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help... Answered by Penny Nom. 





Differentiable on an interval 
20100812 

From Dave: Hi
I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help. Answered by Robert Dawson. 





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 intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





Percent change between two value ranges 
20071128 

From Joe: How do you calculate a percent change between tow value ranges  for instance if I project a range for 2007 to be between 100 and 120 and a range for 2008 to be between 120 and 140, how do I calculate the estimated increase between the range? Is it 0% to 40% (taking the two inside values rto calculate the minimum and the two outside values rto calculate the maximum?) 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. 





Interval of the domain 
20070513 

From Gale: What does the term interval of the domain mean? Answered by Penny Nom and Stephen La Rocque. 





Write the interval in absolute value notation 
20070320 

From Timothy: 1. Write interval in absolute value notation
i) xE[0,9]
ii) xE[2,20] 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. 





Computing confidence intervals 
20041126 

From Christie: I was given a question with N=100, sample proportion is 0.1 compute the 95% confidence interval for P? I have tried this several ways but do not know how to do without means, standard deviations, standard error of the mean? I asked my teacher and she said I have all the info I need. Can you help???? Answered by Penny Nom. 





Sampling distributions 
20020218 

From A student:
 given: n = 40, standard deviation is not known, population of individual observations not normal. does the central limit theorem apply in this case? why or why not?
 for an estimation problem, list two ways of reducing the magnitude of sampling error?
 What will happen to the magnitude of sampling error if the confidence level is raised all other things remaining the same? justify your answer?
Answered by Harley Weston. 





A sample size problem 
20011028 

From Charles: The U.S Transportation Dept. will randomly sample traffic reports to estimate the proportion of accidents involving people over the age of 70. The Dept. has no advance estimate of this proportion. how many reports should the dept select to be atleast 97% confident that the estimate is within .01 of the true proportion? Answered by Harley Weston. 





A confidence interval 
20010628 

From Murray: An investigator wants to find out of there are any difference in "skills" between full and part time students. Records show the following:
Student Mean Score Std Dev Number
   
Full time 83 12 45
Part time 70 15 55
Compute a 95% confidence interval for the difference in mean scores. Answered by Andrei Volodin. 





A confidence interval 
20010426 

From Kim: A poll asked 1528 adults if they were in favor of the death penalty, 1238 said yes, find 99% confidence level for percent of all adult who are in favor of the death penalty. Answered by Andrei Volodin. 





Estimating the population mean 
19991113 

From John Barekman: Statitistics: Estimating the population mean when the standard deviation is known: I am not sure which n to use in the formula for the confidence interval equation: x +/ z*(standard deviation/sqrt(n)) If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples? Answered by Harley Weston. 





La somme de deux fonctions 
20071119 

From maud: Consigne : Ecrire la fonction f comme somme de deux fonctions u et v définies sur I. Donner le sens de variation de u et de v sur I. En déduire le sens de variation de la fonction f sur l'intervalle I indiqué.
f(x)=2x+(1sur x)
I=]0;+infini[
Correction : Sens de variation de f sur I=]0;+infini[
On a f(x)=u(x) + v(x), avec {u(x) = 2x et v(x) = 1sur x
La fonction u est strictement décroissante sur R, donc sur I ( droite avec coefficient directeur 2 négatif).
La fonction v qui est la fonction inverse est stricyement décroissante sur [0;+infini[.
Donc, la fonction f = u+v est strictement décroissante sur [0;+infini[.
Ma question : Pourquoi la fonction v et la fonction f ne sont pas définies sur le même intervalle que la fonction u c'estàdire sur l'intervalle I indiqué ? Answered by Claude Tardif. 

