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Sunday, April 09, 2006 

Scribe for The Day Before yesterday!!!!!!!!!!!!!

Hey folks, sorry i'm a bit late on posting my Scribe post, Computer problems, you see.

Anyways, on friday, we did mostly problems, in preparation for our Pre-Test on Monday. This was helpful, as i now understand what we were doing in this unit.

Here are the Questions:


Let Them Grow!

The Following Data represents the ages of trees drawn as a random sample of trees in a park in manitoba. The DAta were collected by park officials, and the numbers represent the number of rings in the trunk of the tree. Each ring represents one year of growth for a tree.

26 30 48 22 47 42 25 25 29 5 18
4 23 16 36 26 36 35 36 2 39 15
37 29 37 16 15 48 9 12 41 41 32
26 14 5 6 46 21 15 1 26 43 27


(a) Use your calculator to determine the mean, median, range, and standard deviation for the Data.

(b) Use the results of #1 to determine if the sample is normally distributed. Explain your reasoning.

(c) What would the Z-score of a tree with 33 rings be? Explain how you arrived at your answer.

(d) If you assume that the data aer normally distributed, what percentage of trees would have from 17-38 inclusive rings? Explain how you arrived at your answer.




ANSWERS:

(a) 1 var stats (L4)
_
X=27.72
σ=13.4323
Median: 26
Range: 1
σ= 12.295-39.18

(b)16/44=64%
(all within 1
σ)
_
(c)Z=(X-X)/
σ
=.39308
σ is 33 rings


(d) NormalCdf (17,38,27.72,13.4323)
=56.16%

(e)_ _
(X-
1.96σ, X+1.96σ)
-0.6,52.05

%margin of error: (1.96
σ)/n=.598
=59.8% margin of error.



At Aborder Crossing in Canada, customs agents decide which vehicles they will search for undeclared goods as the vehicles enter Canada. Records show that on average 28 percent of the vehicles searched contained undeclared goods.
A New Customs Employee, agent sparks, searched 392 vehicles and found undeclared goods in fewer than one hundred vehicles. The officer in charge, officer Pound, did not do so well in his high school math, but he does know that 28 percent of 392 is about 110 vehicles and so he gave agent sparks a reprimand and a pay cut.

In your opinion, did officer pound do the right thing in giving sparks a pay cut? Carefully explain your reasoning. Support your answer with appropriate statistical information.






ANSWERS:




P=.28
q=1-P
1-.28=.72
q=.72
_
X=np=109.76
σ= (npq)=8.8897



100/392=.25510
invNorm(.25510)
=-.6585

Sum of Prob:
P(<100>
=12.36%



The New Zeppos Are in!


Car Dealer Dan is selling a new car that has just arrived in Manitoba - A Zeppo. He tested 40 cars for gas consumption. and the number of miles per gallon for each car is shown in the table. Assume that the distribution is approximately normal.

30 34 31 33 32 29 31 24 25 33
34 3030 34 29 35 35 33 31 33
36 34 31 32 28 40 29 35 32 33
31 34 29 29 31 39 35 29 32 25


Questions:

(a)Find Mean And Standard Deviation for the Data. Round your answers to one decimal place.

(b)Find the probability that any car selected will have a fuel economy of 35 miles per Gallon (MPG) or better. Round your answer to on decimal Place.

(c) What percent of cars will drive from 27-37 Miles per gallon? He needs this information for his advertising campaign. Round your answer to three decimal places.

(d) Dan anticipates selling 400 zeppos in one year, and wants to offer up a free barbecue to any new car owner whose car does not measure up to a certain level of fuel efficiency. after one year of operation. he does not want to give away more that 20 barbecues. What level of fuel efficiency (in MPG should he guarantee? Round your answer to the nearest whole #.








ANSWERS:


(a)
_
X=32
σ3.46
_
(b) X-X/
σ= Z
(35-32)/3.46
=.867005
NormalCdf(.867005,5)
=.19296, or 19.3%

(c) 27-32/3.46=-1.445
37-32/3.46=1.445
normalCdf(-1.445,1.445)
=.85154, or 85.2%

(d) 20/400
=.05, 0r 5%


invNorm(.05)
=-1.6448536

(1.6448536)(3.46)+32=
26.3088, or 26 MPG he should guarantee if he only gives away 20 barbecues.



Good luck with the Math pre-test on monday morning!




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Good Scribe Nik #1/2. A couple of points to note:

The answer for Let Them Grow!, (b) 16/44 = 64% is incorrect. Of the 44 data points there were 16 outside one standard deviation of the mean.

You did a good job of showing us how to do the calculations. We also need to understand your reasoning. You haven't included any descriptions of your reasoning. I think in class we all felt this was really the hardest part of the question. You're a very articulate guy, why don't you edit in your thoughts. ;-)

I think your inclusion of every question and its solution will be helpful to the whole class as they prepare for the upcoming test. Well done!

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