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Recent problems solved by 'stanbon'
stanbon answered: 57288 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>Next
Rate-of-work-word-problems/286279: Jim can paint a room in 3 hours. Jane can paint the same room in 5 hours. How long will it take if they work together?
1 solutions
Answer 207594 by stanbon(57361)   on 2010-03-28 20:57:18 (Show Source):
You can put this solution on YOUR website!Jim can paint a room in 3 hours. Jane can paint the same room in 5 hours. How long will it take if they work together?
-----------------------
Jim rate: 1/3 room/hr
---
Jane rate: 1/5 room/hr
---
Together rate: 1/x room/hr
=================================
Equation:
rate + rate = together rate:
1/3 + 1/5 = 1/x
(8/15) = 1/x
x = 15/8
x = 1 (7/8) hrs (time to do the job together)
===============================================
Cheers,
Stan H.
|
Rational-functions/286276: Find all the zeros of the function:
p(x)=X^3-2x^2+9x-18
1 solutions
Answer 207591 by stanbon(57361) on 2010-03-28 20:53:17 (Show Source):
You can put this solution on YOUR website!Find all the zeros of the function:
p(x)=X^3-2x^2+9x-18
---
I graphed it and found it has a zero at x = 2
---
Use synthetic division to find the quotient:
2)...1....-2....9....-18
.....1.....0....9....|..0
------------------
Quotient: x^2 +9
-----
Factor the quotient:
(x+3i)(x-3i) = 0
---
Zeroes: 2 or -3i or +3i
============================
Cheers,
Stan H.
============================
|
Probability-and-statistics/286238: The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 92% confident that our sample mean is within 1 IQ points of the true mean. The mean for this population is clearly greater than 100 . The standard deviation for this population is probably less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use σ = 15, we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that σ = 15 and determine the required sample size.
1 solutions
Answer 207585 by stanbon(57361) on 2010-03-28 20:44:16 (Show Source):
You can put this solution on YOUR website! The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 92% confident that our sample mean is within 1 IQ points of the true mean. The mean for this population is clearly greater than 100 . The standard deviation for this population is probably less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use σ = 15, we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that σ = 15 and determine the required sample size.
-----------------
n = [z*s/E]^2
For your problem the required z value has
2 tails each of 0.04.
invNorm(0.96) = 1.7507
-----
n = [1.7507*15/1]^2
---
n = 689.6
Round up to get: n = 690
===============================
Cheers,
Stan H.
|
Average/286241: What is the cruising speed of the CD-10?
1 solutions
Answer 207580 by stanbon(57361) on 2010-03-28 20:22:09 (Show Source):
You can put this solution on YOUR website!Q1) |2x-1|>5 for x.
Solve 2x-1<-5 or 2x-1>5
2x < -4 or 2x > 6
x < -2 or x > 3
------------------------------
Q2) Sketch the graph of the equation y= 2x^2 - 8x + 11 using the intercepts and vertex.
----
Vertex at x = -b/2a = 8/4 = 2
f(2) = 2(4)-8(2)+11 = 3
Vertex: (2,3)
------------
y-intercept when x = 0
(0,11)
--------------------
Sketch:
----------------------------------------------------
Q3) tan(theta) = - square root of 3, find (theta) for 0 < (theta) < 2 pie
x = tan^-1(-sqrt(3)) = 300 degrees or 120 degrees
===========================
Cheers,
Stan H.
===========================
|
test/286266: . Use 4 and 5 as the first two terms of a Fibonacci-type sequence.
Find the next five terms?
1 solutions
Answer 207579 by stanbon(57361) on 2010-03-28 20:12:14 (Show Source):
You can put this solution on YOUR website!Use 4 and 5 as the first two terms of a Fibonacci-type sequence.
Find the next five terms?
-
1st: 4
2nd: 5
3rd: 4+5=9
4th: 5+9 = 14
5th: 9+14 = 23
=================
Cheers,
Stan H.
|
Graphs/286263: graph the inequality on a plane.
5x + 6y 'is less than or equal to' 30
I am sure this is a simple solution, but I am terrible with finding the answers...the graphing part I'm ok with?? Thank you in advance.
1 solutions
Answer 207577 by stanbon(57361) on 2010-03-28 20:10:17 (Show Source):
You can put this solution on YOUR website!graph the inequality on a plane.
5x + 6y 'is less than or equal to' 30
I am sure this is a simple solution, but I am terrible with finding the answers...the graphing part I'm ok with?? Thank you in advance.
-------------------
Graph the EQUALITY, which is the boundary of the INEQUALITY:
5x+6y = 30
y = (-5/6)x + 5
--------------------
Plot points (0,5) and (6,0) and
draw a line thru them.
---------
Shade the half-plane BELOW the boundary because
you want the y-values LESS THAN the boundary line y-values.
================
================
Cheers,
Stan H.
|
Triangles/286259: The three sides of a triangle are 7, 24, and 30 units long. Is the triangle acute, right or obtuse? You must support your answer with computations.
1 solutions
Answer 207573 by stanbon(57361) on 2010-03-28 19:59:53 (Show Source):
You can put this solution on YOUR website!The three sides of a triangle are 7, 24, and 30 units long. Is the triangle acute, right or obtuse? You must support your answer with computations.
-----------------------------------------------
Use the Law of Cosines:
cos(A) = (7^2 + 24^2-30^2)/(2*7*24) = -0.81845
---
A = cos^-1(-0.81845) = 144.94 degrees
------------------------------------------
cos(B) = (30^2+7^2-24^2)/(2*30*7)
cos(B) = 0.8881
---
B = cos^-1(0.8881) = 27.37 degrees
-------------
cos(C) = (30^2+24^2-7^2)/(2*30*24) = 0.9910
C = cos^-1(0.9910) = 7.70 degrees
========================================
Cheers,
Stan H.
|
Exponents/286256: I really don't even know where to begin with this problem.
Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.
0.4^x=343
1 solutions
Answer 207571 by stanbon(57361) on 2010-03-28 19:43:40 (Show Source):
You can put this solution on YOUR website!Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.
0.4^x=343
[2^2/2*5]^x = 7^3
---------------------------
Rewrite in terms of a and b:
(2^2/(2*2^a))^x = (2^b)^3
(2^2/2(a+1))^x = 2^(3b)
(2^(1-a))^x = 2^(3b)
(2^(x(1-a)) = 2^3b
-----------------------
Equate the exponents and solve for "x":
x(1-a) = 3b
x = (3b)/(1-a)
===================
Cheers,
Stan H.
======================
|
Equations/286253: Hi, I'm supposed to simplify this if possible.
((1/(x+h)^2)-(1/x^2))/h
I've tried several ways of solving this, most recently coming up with the answer (1-2xh-h^2)/(x^2h+2xh^2+h^3) but this isn't right. Can someone please help me?
1 solutions
Answer 207563 by stanbon(57361) on 2010-03-28 19:23:36 (Show Source):
You can put this solution on YOUR website!simplify this if possible.
((1/(x+h)^2)-(1/x^2))/h
-------------------
lcd = x^2(x+h)^2
Rewrite each fraction with the lcd as its denominator:
------------------------
[(x^2/lcd - (x+h)^2/lcd]/h
Combiine the numerators over the lcd:
---------------------
[x^2 -x^2-2hx-h^2]/(lcd*h)
Simplify the numerator:
-------------------------
(2hx-h^2)/(lcd*h)
Divide by "h" to get:
---
= (2x-h)/(x^2(x+h)^2)
---------------------------
Cheers,
Stan H.
|
Probability-and-statistics/286131: I sent the below question in last night. I know my Xbar is 20.4, my S is .5 and my CI is 95% I am trying to solve for n correct? The only equation my stats teacher taught us last week is t = xbar - mu over s/square root of n.....I can't find n without t so i don't know how to start this. I don't need you to solve it for me just point me in the direction of how to find either t or n and I can solve it. Thank you.
A processor of carrots cuts the green top off each carrot, washes the carrots,
and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation .5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than .2 pound?
1 solutions
Answer 207562 by stanbon(57361) on 2010-03-28 19:15:47 (Show Source):
You can put this solution on YOUR website!A processor of carrots cuts the green top off each carrot, washes the carrots,
and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation .5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than .2 pound?
---------
The formula for sample sample size is derived from the
formula for standard error.
----
Since E = z*s/sqrt(n)
---
n = [z*s/E]^2
----
Your Problem:
n = [1.96*0.5/0.2]^2 = 24.01
Rounding up, n = 25
==========================
Cheers,
Stan H.
|
Probability-and-statistics/286222: After the first exam the professor reports to the class that the mean for the exam was 73, and the standard deviation was 7.
If the bottom 10% of the class fail the exam, what score would earn a student a failing grade?
1 solutions
Answer 207545 by stanbon(57361) on 2010-03-28 18:27:33 (Show Source):
You can put this solution on YOUR website!After the first exam the professor reports to the class that the mean for the exam was 73, and the standard deviation was 7.
If the bottom 10% of the class fail the exam, what score would earn a student a failing grade?
--------------------
Find the z-value with a 10% left tail:
invNorm(0.10) = -1.2816...
-------------------
Find the score corresponding to that z-score:
------
x = zs+u
x = -1.2816*7 + 73
x = 64.029
Scores below that fail.
===============================
Cheers,
Stan H.
|
Triangles/286186: okay so in a right triangle the degree measures of the acute angles are in the ratio of 2:3. the degree measure of the smallest angle is___.
please tell me how to solve this problem
1 solutions
Answer 207511 by stanbon(57361) on 2010-03-28 16:41:36 (Show Source):
You can put this solution on YOUR website! okay so in a right triangle the degree measures of the acute angles are in the ratio of 2:3. the degree measure of the smallest angle is___.
please tell me how to solve this problem
---------------
Those two acute angles are complementary; they add up to 90 degrees.
---
2:3 is the same as 2x to 3x
-----------------------------
Equation:
2x + 3x = 90 degrees
5x = 90 degrees
x = 18 degrees
----------------
The smaller angle is 2x = 2*18 = 36 degrees.
===============================================
Cheers,
Stan H.
|
Graphs/286100: How do you graph a line symmetric to another line?
1 solutions
Answer 207509 by stanbon(57361) on 2010-03-28 16:38:49 (Show Source):
You can put this solution on YOUR website!How do you graph a line symmetric to another line?
-------------
1st: You need to identify an axis for the symmetry.
2nd: For two points of the given line, draw a line
segment perpendicular to the axis of symmetry and
an equal distance beyond it. Put a point at the
end of that segment.
3rd: Draw a line thru those two end points.
-----
Result: The resulting line will be symmetric
to the given line with repect to the axis of
symmetry.
===============================
Cheers,
Stan H.
===============================
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Probability-and-statistics/286164: A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all of the households in her city being monitored by the TV industry would tune in to the new show? Assume that the households constitute a random sample of American households.
Round your response to at least three decimal places.
1 solutions
Answer 207506 by stanbon(57361) on 2010-03-28 16:31:45 (Show Source):
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percentage/286118: linda bought a pair of trainers when there was 20% off the normal price. she paid £18.00 for them. what was the normal price for the trainers?
1 solutions
Answer 207461 by stanbon(57361) on 2010-03-28 13:41:13 (Show Source):
You can put this solution on YOUR website!linda bought a pair of trainers when there was 20% off the normal price. she paid £18.00 for them. what was the normal price for the trainers?
------------------
Let the normal price be "x":
x - 0.20x = 18
---
0.80x = 18
----
x = 22.50
=============
Cheers,
Stan H.
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Probability-and-statistics/286115: If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat?
1 solutions
Answer 207459 by stanbon(57361) on 2010-03-28 13:38:15 (Show Source):
You can put this solution on YOUR website! If a baseball player's batting average is 0.340 or 34%, find the probability that the player will have a bad season and only score at most 60 hits in 200 times at bat?
--------
Binomial Problem with n= 200 ; p = 0.34 ; x = 60
---------------------
P(x=60) = 200C60*(0.34)^60*(0.66)^140 = 0.02968...
-----------------
Cheers,
Stan H.
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Travel_Word_Problems/286107: A car traveled 175 miles at a certain speed. If the speed had been 20 mph faster, the trip could of been made in one less hour. Find the speed of the car.
I have both the distances as 175 i have one rate as r and the other rate as r+20 then the car with the rate of r and have as t time and the car with the rate of r+20 i have the time a t-1 is this right?
1 solutions
Answer 207458 by stanbon(57361) on 2010-03-28 13:34:09 (Show Source):
You can put this solution on YOUR website! A car traveled 175 miles at a certain speed. If the speed had been 20 mph faster, the trip could of been made in one less hour. Find the speed of the car.
---
Slower speed DATA:
distance = 175 miles ; rate = r mph ; time = 175/r hrs.
----------------------------------------------
Faster speed DATA:
distance = 175 miles ; rate = r+20 mph ; time = 175/(r+20) hrs
----------------------------------------------
Equation:
slow time - fast time = 1 hr
175/r - 175/(r+20) = 1
---
Multiply thru by r(r+20):
175(r+20) - 175r = r(r+20)
175*20 = r^2 + 20r
--------------------------
r^2 + 20r - 175*20 = 0
---
(r+70)(r-50) = 0
Positive solution
rate = 50 mph (slower rate)
r+20 = 70 mph (faster rate)
================================
Cheers,
Stan H.
================================
I have both the distances as 175 i have one rate as r and the other rate as r+20 then the car with the rate of r and have as t time and the car with the rate of r+20 i have the time a t-1 is this right?
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Equations/286104: ok my teacher gave us words problmes to do and im stuck. Here is the problem: Bill is 3 times as old as Peter. Six years from now, Bill will be twice as old as Peter will be then. Find their present ages. Im stuck on what the formula is.
1 solutions
Answer 207454 by stanbon(57361) on 2010-03-28 13:19:00 (Show Source):
You can put this solution on YOUR website!Bill is 3 times as old as Peter.
b = 3p
-------------------
Six years from now, Bill will be twice as old as Peter will be then.
(b+6) = 2(p+6)
---------------------------
Substitute for "b" and solve for "p":
(3p+6) = 2(p+6)
3p+6 = 2p+12
p = 6 (peter's age now)
---
Since b = 3p,
b = 18 (bill'e age now)
=============================
Cheers,
Stan H.
Find their present ages.
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Probability-and-statistics/286095: You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5. Test the hypothesis using an alpha of 5%. Use formal hypothesis testing and compute the p-value.
1 solutions
Answer 207453 by stanbon(57361) on 2010-03-28 13:14:25 (Show Source):
You can put this solution on YOUR website!You want to prove that a population mean is not 7.
Data is ratio and a large sample size will be used (n = 225).
When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5.
Test the hypothesis using an alpha of 5%.
Use formal hypothesis testing and compute the p-value.
-----
Ho: u = 7
Ha: u is not 7 (claim)
-------------------------------
t(7.2) = (7.2-7)/1.5 = 0.1333...
---
p-value = 2*P(t > 0.13333.. with df = 224)
= 2*tcdf(0.13333..,100,224) = 0.8940
----
Wow! Fail to reject Ho; that p-value is much larger than the p-value.
=================================================
Cheers,
Stan H.
=================================================
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Triangles/286027: A triangle has three angles with measurements A, B, and C such that A = x^2 + 49,
B = x + 2, and C = x + 130. Assume all angles are measured in degrees. Find x.
A. x = 0 B. x = 1 C. x = 180 D. x = −1 E. None of these.
1 solutions
Answer 207422 by stanbon(57361) on 2010-03-28 09:52:28 (Show Source):
You can put this solution on YOUR website! A triangle has three angles with measurements A, B, and C such that
A = x^2 + 49, B = x + 2, and C = x + 130.
Assume all angles are measured in degrees. Find x.
---------------------
Equation:
A + B + C = 180 degrees
(x^2+49) + (x+2) + (x+130) = 180
---
x^2 + 2x + 181 = 180
---
x^2 + 2x + 1 = 0
(x+1)^2 = 0
x = -1
-----
A = x^2+49 = 50 degrees
B = x+2 = 1 degree
C = x + 130 = 129 degrees
============================
Cheers,
Stan H.
============================
A. x = 0 B. x = 1 C. x = 180 D. x = −1 E. None of these.
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Linear_Equations_And_Systems_Word_Problems/286043: The sales representative informs you that there are two floor plans still available, and that there are a total of 63 houses available. The sales representative later indicates that there are six times as many homes available with the second floor plan than the first. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2.
(I keep finding myself struggling with these I really have no idea where to start. Thanks in advance for helping me, I really appreciate it, more than you'll ever know!!)
1 solutions
Answer 207419 by stanbon(57361) on 2010-03-28 09:38:50 (Show Source):
You can put this solution on YOUR website!The sales representative informs you that there are two floor plans still available, and that there are a total of 63 houses available. The sales representative later indicates that there are six times as many homes available with the second floor plan than the first. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2.
(I keep finding myself struggling with these I really have no idea where to start. Thanks in advance for helping me, I really appreciate it, more than you'll ever know!!)
----------------------------------
Quantity Equation: x + y = 63
Quantity Equation: y = 6x
==================================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/286044: The sales representative here tells you they also have two floor plans available, but they only have 42 homes available. The representative tells you that floor plan #1 sells for $100,000 and floor plan #2 sells for $150,000. She also mentions that all the available houses combined are worth $6 million. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2.
( I think the equations would be x + 100,000 = 6,000,000 and y + 150,000 =6,000,000 But im second guessing myself.)
1 solutions
Answer 207418 by stanbon(57361) on 2010-03-28 09:36:25 (Show Source):
You can put this solution on YOUR website!The sales representative here tells you they also have two floor plans available, but they only have 42 homes available. The representative tells you that floor plan #1 sells for $100,000 and floor plan #2 sells for $150,000. She also mentions that all the available houses combined are worth $6 million. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2.
( I think the equations would be x + 100,000 = 6,000,000 and y + 150,000 =6,000,000 But im second guessing myself.)
-------------------------------------------------
Quantity Equation: x + y = 42
Value equation:100,000x + 150,000y = 6,000,000
------------------------------------------------------
Cheers,
Stan H.
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Square-cubic-other-roots/286045: Simplify each expresion. Rationalize all denominators. Assume that all variables are positive of the equation
sqrt(20) – 3sqrt(5) + sqrt(45)
1 solutions
Answer 207417 by stanbon(57361) on 2010-03-28 09:33:46 (Show Source):
You can put this solution on YOUR website! Assume that all variables are positive of the equation
sqrt(20) – 3sqrt(5) + sqrt(45)
------------------------------------
Rewrite as:
sqrt(4*5) - 3*sqrt(5) + sqrt(9*5)
---
= 2sqrt(5) - 3sqrt(5) + 3sqrt(5)
---
= (2-3+3)sqrt(5)
---
= 2sqrt(5)
===================
Cheers,
Stan H.
===================
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Number-Line/286049: 3x-y=3
with x-0 and y-6
My answer is 3, I don't get why answer is -1, can you give me steps
1 solutions
Answer 207416 by stanbon(57361) on 2010-03-28 09:30:59 (Show Source):
You can put this solution on YOUR website!3x-y=3
with x-0 and y-6
My answer is 3, I don't get why answer is -1, can you give me steps
--------------------------------
Note: What do you mean by "x-0" and "y-6"??
How did you get an answer of "3"??
Cheers,
Stan H.
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Probability-and-statistics/286006: a box contains 6 red,4 white and 5 black balls .A person draws 4 balls from the box at random. find the probability among the balls drawn there is at least one ball of each color
1 solutions
Answer 207414 by stanbon(57361) on 2010-03-28 09:27:45 (Show Source):
You can put this solution on YOUR website!A box contains 6 red, 4 white and 5 black balls.
A person draws 4 balls from the box at random.
A find the probability among the balls drawn there is at least one ball of each color
-------
Ans: 1 - P(no red or no white or no black)
---
= 1 - [P(no red)+P(no white)+P(no black)]
---
= 1 - [9C4 + 11C4 + 10C4]/15C4
---
= 1 - 666/1365
---
= 0.5121....
Cheers,
Stan H.
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Probability-and-statistics/285981: in Rivendell memorial hospital the time to complete surgery in a routine tubal ligation without complication is normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. The next procedure has been scheduled in the same operating room 60 minutes after the beginning of a tubal ligation procedure.
Allowing 20 minutes to vacate and prepare the operating room between procedures, what is the probability that the next procedure will have to be delayed?
1 solutions
Answer 207386 by stanbon(57361) on 2010-03-27 22:55:04 (Show Source):
You can put this solution on YOUR website!in Rivendell memorial hospital the time to complete surgery in a routine tubal ligation without complication is normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. The next procedure has been scheduled in the same operating room 60 minutes after the beginning of a tubal ligation procedure.
Allowing 20 minutes to vacate and prepare the operating room between procedures, what is the probability that the next procedure will have to be delayed?
--------------------
If tubal ligation takes > 40 min (procedure delayed)
------------------------------------
z(40) = (40-30)/8 = 5/4
------
P(procedure delayed) = P(x>40) = P(z> 5/4) = normalcdf(5/4,100) = 0.1056
=================================
Cheers,
Stan H.
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Probability-and-statistics/285982: passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.
Determine:
a. mean swipe rate - i got 27.5
b. standard deviation of the swipe rate - i got 12.99
c. 1st quartile
d. third quartile
e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range?
Not sure about quartiles and e., and hope a. and b. are correct
1 solutions
Answer 207384 by stanbon(57361) on 2010-03-27 22:19:50 (Show Source):
You can put this solution on YOUR website!passengers using new york's metrocard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader.
---
Draw a picture of the uniform distribution.
Base has width 50-5 = 45
Therefore height = 1/45
-------------------------------
Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.
Determine:
a. mean swipe rate - (50-5)/2 = 27.5
--------------------------------------------
b. standard deviation of the swipe rate - i got 12.99
Note: I'm not sure how you got 12.99.
The formula I find is sqrt[[(50-5)+1]^2 -1]/12] = sqrt[[46^2-1]/12] = 13.28
---------------------------------------------
c. 1st quartile
Point with left tail = 0.25
base(1/45) = 0.25
base = 45*0.25
base = 11.25
But base starts at 5 so the 1st quartile value is 5+11.25 = 16.25
-------------------------------
d. third quartile
Point with left tail of 0.75
base(1/45) = 0.75
base = 45*0.75
base = 33.75
But base starts at 5 so the 3rd quartile value is 5+33.75 = 38.75
-------------------------------
e. what percentage of subway riders must re-swipe the card because they were outside the acceptable range?
Ans: 1 - P(10<= x <=40) = 1 - (30/45) = 1 - 2/3 = 1/3 = 33.33%
---------------------------------
Cheers,
Stan H.
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Probability-and-statistics/285933: Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why?
Correct? Regular Cola Diet Cola Row Total
Yes, got it right 7 7 14
No, got it wrong 12 20 32
=============================================
Col Total 19 27 46
1 solutions
Answer 207360 by stanbon(57361) on 2010-03-27 20:38:21 (Show Source):
You can put this solution on YOUR website!Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample
z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why?
Yes got it right - 7, 7, 14
no got it wrong - 12, 20, 32
total - 19, 27, 46
-----------------
Chi-Sq Test:
Ho: the columns are homogeneous
Ha; the columns are not homogeneous
Using a TI-calculator Chi-Sq Test I get:
Test statistic: Chi-Sq = 0.62768....
p-value = 0.428..
--------
Conclusion: Reject Ho;
The columns are not homogeneous
=======================================
Two-tailed sample z test:
Ho: mu1 = mu2
Ha: mu1 is not equal to mu2
Critical value for 2-tailed test and alpha=5%: +-1.96
--------
x1-bar = 19/2= 9.5
x2-bar = 27/2= 13.5
sigma1^2 =7.77817^2 = 60.5
n1=19
sigma2^2 =9.1924^2=84.5
n2=27
---------------
z(9.5-13.5)/sqrt[(60.5/19) + (84.5)/27] = -1.59
p-value = 2P(-10 < z <-1.59) = 0.1118...
--------
Conclusion: Since p-value > alpha, Fail to Reject Ho.
The columns are homogeneous.
-----------------------------
As you see, the test results are not the same.
I'll leave the discussion of the final questions to you.
-----------------------------
Cheers,
Stan H.
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