probability questions
Solution
Click Link Below To Buy:
Contact Us:
Hwcoursehelp@gmail.com
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.
No comments:
Post a Comment