The Math Help Column
Solutions to Your Everyday Math Dilemmas
Enter a response to each question.
1) Dear Math Helper,
I am in need of your help! I have a job where I design games. I am designing a game that involves a
playing area with 12 equal sections. Players randomly end up in one of the sections.
I labeled one section, "Gain 40 points," four sections, "Gain 10 points," and the rest, "Try Again." Also,
each player automatically gives up 10 points with each move.
After trying out the game on some volunteers, I noticed that players tend to lose points in the long run.
Without changing the sizes of the sections, what adjustments can I make so that players are likely to earn
at least one point, in the long run?
Signed,
Game Maker
Dear Game Maker,
*Type your response here.
2) Dear Math Helper,
First, let me tell you how much I enjoy your column. It is the first thing I read in every issue.
I run a carpet cleaning company and need some advice. I want to offer steam cleaner rentals, because
some people prefer to save money by cleaning their own carpets. But steam cleaners are expensive and
they need repairs if not used properly, so I'm going to offer insurance policies. I'm not sure how much to
charge.
It will cost me $190 to replace one of my cleaners, and repairs average $100. I talked to some other
people I know in the business and they said I should expect to replace a cleaner for about 1 of every 50
rentals and to repair a cleaner for about 1 of every 20 rentals. I'm not sure what to do with all this
information.
Please help me determine a fair price for my insurance policy. I want my rates to be low enough that
customers buy the insurance, but high enough that I don't lose money by offering it. And please show me
how you came up with your figure, so that I can make adjustments later if I need to.
Your number one fan,
Steaming in Seattle
Dear Steaming in Seattle,
*Type your response here.
3) Dear Math Helper,
I work in construction and am pretty good in math, especially with fractions, so I didn't think I would ever
have to write to you. But this one has got me stumped.
Last week I bought two boxes of nails, each from a different manufacturer. I poured the nails from one
box into my left pocket and the other into my right. I started to use the ones in my left pocket, but they
kept breaking and bending. I will never use them again. But here's my problem. I don't remember which
box they came from.
I contacted both manufacturers and "Manufacturer A" said their boxes have a mean of 205.4 nails and a
standard deviation of 1.8 nails. "Manufacturer B" said their boxes have a mean of 190.6 nails and a
standard deviation of 3.3 nails. Both said their number of nails is normally distributed.
I counted the nails from my left pocket, including the used ones, and got 198. This is 7.4 nails less than
Manufacturer A and 7.4 nails more than Manufacturer B. So I guess the standard deviation comes into
play, but I don't know how.
Please explain which manufacturer most likely made these defective nails.
Sincerely,
Stumped Builder
Dear Stumped Builder,
*Type your response here.
4) Dear Math Helper,
Please help settle this friendly dispute.
My friend, let's call her Pam, took the same history course I did, but we had different professors. On the
final exam, I scored 82 out of 100 points while she scored 47 out of 63 points.
My percent score, 82%, is greater than her percent score, which is about 75%. So I think I did better than
she did on the final exam.
But she tells me that both sets of scores are normally distributed and that I have to look at the standard
scores to find out who did better. Pam tells me that the mean and standard deviation for my test are 76.1
and 6.5, respectively, while hers are 40 and 4.2 respectively, so if I "do the math," then I should see why
she performed better.
Can you please explain what she means by standard scores and can you "do the math" that she
mentions.
Yours,
Confused History Buff
P.S. If she did perform better, I have to buy her dinner!
Dear Confused History Buff,
*Type your response here.
5)Dear Math Helper,
You write a great column, and I hope you stay around for years to come.
I run a small boarding school. We are going to begin using test scores to help determine admissions
eligibility. The scores for the test I have in mind are normally distributed with a mean of 300 and a
standard deviation of 12.5. Can you show me how to determine the cutoff score if we should use to only
accept only applicants who score in the top 10% on the test? What cutoff score includes the top 15%?
Thanks in advance.
Regards,
The Student Selector
Dear Student Selector,
*Type your response here.
6) Dear Math Helper,
How's it going? I'm in the business of printing T-shirts and just got an interesting order.
My sister is pre-med student and wants to show off how well she performed on the Medical College
Admission Test (MCAT). I told her I’d make her a T-shirt, but she’s not making it easy for me.
She wants the back of the shirt to read, "I scored at the nth percentile on the MCAT!" But instead of
giving me the value of n, she told me her individual score was 38 and that all the test scores are normally
distributed with a mean of 25 and a standard deviation of 6.4.
I don’t want to let her think she’s smarter than me, even if she is going to be a doctor! Can you explain
how I should use these numbers to find the value of n for her shirt? If so, maybe there's a free T-shirt in
your future!
Many thanks,
T-shirt Guy
Dear T-shirt Guy,
*Type your response here.