







Percentage change in refractive error 
20190404 

From Ammara: Hi, I'm trying to figure out how a paper I'm looking at has found a percentage from the numbers below. its a paper comparing two lenses. it says that the new lenses 'slowed the progression of refractive error by approximately 50%'.
the refractive error with the old lenses was 2.26 after two years it was 3.28
the refractive error with the new lenses was 2.24 after two years the refractive error is  2.75
Thank you so much for your help it is most appreciated! Answered by Penny Nom. 





Why does 10x10x10 give 1,000.0000000000001? 
20170412 

From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom. 





An error in finding the mean 
20130225 

From Abhishek: Mean of 50 observations was found to be 80.4 but later all it was discovered 96 was mistake at 69
Find the correct mean? Answered by Penny Nom. 





Transposition error 
20121203 

From Carol: What is the correct term for when a child writes 61 instead of 16, or 83 for 38when they switch the place values of a number? Answered by Chris Fisher. 





Vapor trails 
20100412 

From Frank: I'm not sure if this is a proper question to ask so if I have misdirected my question I apologize and no response is expected. I am trying to figure out a way to measure vapor trails from my back yard in Phoenix Arizona. If I used a compass and spread each point of the compass to the start and finish of the vapor trail I would have the angle of an isosceles triangle. The other two angles would be identical. The height of from the inverted base of the triangle to my standing spot on the ground would be about 35,000 feet. I'm thinking that there should be a way to figure out the length of the inverted base (vapor trail) but I'm devoid of mathematical skills and can't seem to figure out how to do this. Is it possible to figure out the length of a vapor trail using this method or do you have an easier way to accomplish the task?
Any help you could offer would be most appreciated.
Thanks....Frank Answered by Harley Weston. 





The integral of a to power x squared 
20090428 

From JIM: WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO
WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE
SOLVED : a to power x squared . is this still true ?
CURIOUS , JIM Answered by Robert Dawson. 





The sum is 43 and the difference is 9 
20090302 

From Teresa: Hi, My 10yo son came home with this two problems and we can't figure out how to solve them.
1. Find two numbers whose sum is 43 and whose difference is 9 and
2. Find two numbers whose sum is 25 and whose difference is 11..
Many thanks
Teresa Answered by Robert Dawson, Stephen La Rocque and Harley Weston. 





Confidence level 
20071119 

From Fara: It is common for public opinion polls to have a " confidence level" of 95%, meaning
that there is a 0.95 probability that the poll results are accurate within the claimed margins of error.
If six different organizations conduct independent polls, what is the probability that all
six of them are accurate within the claimed margins of error? Does the results suggest that
with a confidence level of 95%, we can expect that almost all polls will be within the claimed
margin of error? Answered by Harley Weston. 





Percent difference 
20070517 

From Carolyn: What is the % difference between these two numbers 211373 & 185420 Answered by Gabriel Potter, Penny Nom and Steve La Rocque. 





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. 





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. 





Numerical problems 
20011127 

From Yossi: I am preparing a 45 minutes class for K12 students. The problem is to show that algebraic equivalent expressions are not always numerically equivalent. In particular I would like to show one of these dangers: cancellation that occurs during the subtraction of nearly equal quantities. Do you have a good reference I could use to prepare my class. In particular to be able to show some examples and how one can avoid this type of error. I also would like to show examples with practical use. I tried to look up in the web but did not find anyhting appropriate. Answered by Chris Fisher. 





Renee, Paulo and Peter 
20011118 

From Sue: Renee is 5 years older than Paulo. she is also 7 years older than Peter. The sum of their ages is 21. How old is each person. Answered by Penny Nom. 





Linear regression 
20010801 

From A student and a mother: My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation rxy and standard estimate of errorSy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related. Answered by Chris Fisher and Penny Nom. 





Margin of error 
20010713 

From Jim: If a survey was completed by four different groups of people as indicated below what would the overall margin of error be for this survey given the fact that the number of people in each group were different?
Group # polled Margin of error
A. 779 +/ 4%
B. 315 +/ 7%
C. 323 +/ 6%
D. 254 +/ 9%
Answered by Andrei Volodin. 





What is wrong with these probelms? 
20010209 

From Cindy: Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Error in patterns: 13/35=1/5; 27/73=2/3; 16/64=1/4 4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11 2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10 Answered by Leeanne Boehm and Penny Nom. 





Two problems 
20001102 

From Michael: Question: I mistakenly divided a number by 5 when I should have multiplied by 5. FInd my percent of error. Next Question: How many odd numbers are between 10 and 9,999 from the digits 09 if each digit is used once per number. Answered by Penny Nom. 





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. 





The three cousins 
19990601 

From Irena: I have three cousins on my dad's side. The product of their ages is 84. Next year the youngest will be 1/4 the age of the middle cousin. In 2 years from now, the oldest will be twice the current age of the middle. What is the age of my oldest cousin? Answered by Harley Weston. 





Intersecting Lines. 
19980210 

From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, 4186) and (770, 1816) respectively. How can that be? Answered by Penny nom. 

