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Recent problems solved by 'stanbon'
stanbon answered: 57151 problems
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54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextProbability-and-statistics/575674: 4. A basket contains 3 red,4 white and 7 yellow beads. Three beads are taken at random without replacement. Calculate the probability of getting
i. Three beads of the same colour (2 marks)
ii. At least two white beads (2marks)
iii) A red bead followed by a yellow bead. (3marks)
1 solutions
Answer 369588 by stanbon(57219)   on 2012-02-21 12:18:08 (Show Source):
You can put this solution on YOUR website!A basket contains 3 red,4 white and 7 yellow beads. Three beads are taken at random without replacement. Calculate the probability of getting
i. Three beads of the same colour (2 marks)
# of ways to succeed: 3C3+4C3+7C3 = 1 + 4 + 35 = 40
# of random results: 14C3 = 364
P(3 same color) = 40/364
------------------------------------------
ii. At least two white beads (2marks)
# of ways to succeed: 4C2 + 4C3 + 4C4 = 6 + 4 + 1 = 11
# of random results: 364
P(at least 2 white) = 11/364
-------------------------------------------------
iii) A red bead followed by a yellow bead. (3marks)
P(yellow | red) = (3/14)(7/13) = 3/26
==========================================
Cheers,
Stan H.
=================
|
Probability-and-statistics/575676: A single card is selected from an ordinary deck of cards. The sample space is shown in the following figure. Find the following probabilities.
P(5 and a Jack)
P(5 or a Jack)
P(Heart or a Jack)
1 solutions
Answer 369586 by stanbon(57219) on 2012-02-21 12:12:36 (Show Source):
|
Probability-and-statistics/575691: . An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 778 and 834 hours.
1 solutions
Answer 369585 by stanbon(57219) on 2012-02-21 12:11:31 (Show Source):
You can put this solution on YOUR website!An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 778 and 834.
---------------
Using z-calculations:
z(778) = (778-800)/40 = -0.55
z(834) = (834-800)/40 = 0.85
P(778<= x <=834) = P(-0.55<= z <=0.85) = normalcdf(-0.55,0.85) = 0.5112
==================================================
Using a TI-84:
normalcdf(778,834,800,40) = 0.5112
===============
Cheers,
Stan H.
===============
|
Probability-and-statistics/575646: for each hypothesis listed indicate:
Whether the appropriate analysis would be a one-tailed test or a two-tailed test.
A type I and type II error, given the context of the hypothesis.
Hypothesis:
The three treatments tested differ in how well they work.
Children receiving supportive therapy will get worse over time (at posttreatment).
Girls will do better than boys with treatment (any treatment).
1 solutions
Answer 369579 by stanbon(57219) on 2012-02-21 10:09:32 (Show Source):
You can put this solution on YOUR website!for each hypothesis listed indicate:
Whether the appropriate analysis would be a one-tailed test or a two-tailed test.
A type I and type II error, given the context of the hypothesis.
Hypothesis:
The three treatments tested differ in how well they work.:: 2-tail
Type I:Reject Ho when it is correct.
Type II: Fail to reject Ho when it is incorrect.
--------------------------------------------
Children receiving supportive therapy will get worse over time (at posttreatment).:: right-tail test
---------------------------------------
Girls will do better than boys with treatment (any treatment).
:: right-tail test
=============================
Cheers,
Stan H.
|
Probability-and-statistics/575536: What is the probability that two people choices will be greater than 75. choose from 1 to 90
1 solutions
Answer 369577 by stanbon(57219) on 2012-02-21 10:02:53 (Show Source):
You can put this solution on YOUR website!What is the probability that two people choices will be greater than 75. choose from 1 to 90
---
P(1st person chooses above 75) = 15/90 = 1/6
P(2nd person chooses above 75) = 1/6
=====
P(both do) = (1/6)^2 = 1/36
===========================
Cheers,
Stan H.
|
Probability-and-statistics/575628: This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many chairs did the carpenter make?
1 solutions
Answer 369575 by stanbon(57219) on 2012-02-21 09:55:37 (Show Source):
You can put this solution on YOUR website!This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many chairs did the carpenter make?
--------
# of stools EQ: t + f = 30
# of legs EQ:: 3t +4f = 103
-------------------
Multiply thru stools EQ be 3 to get:
3t + 3f = 3*30
3t + 4f = 103
----
subtract and solve for "f":
f = 13 (# of four-legged stools)
---
Solve for "t":
t + f = 30
t + 13 = 30
t = 17 (# of 3-legged stools)
===============================
Cheers,
Stan H.
|
Money_Word_Problems/575636: find the principle when :
final amount =4500 at 20 %per annum in 5 years
1 solutions
Answer 369568 by stanbon(57219) on 2012-02-21 09:45:01 (Show Source):
You can put this solution on YOUR website!find the principle when :
final amount =4500 at 20 %per annum in 5 years
------
A(t) = P(1+rt)
4500 = P(1+0.2*5)
4500 = P(1+1)
P = 4500/2
Priciple = $2250
===================
Cheers,
Stan H.
===================
|
Probability-and-statistics/575425: I am an instructor at a high school and just gave a fifty item multiple choice exam (a,b,c,d). Five students who sit together at a table got the same 8 of the 50 questions wrong. What is the probability of that happening? I want to be able to support the fact that I believe they cheated. Thanks!
Top
1 solutions
Answer 369516 by stanbon(57219) on 2012-02-20 22:14:58 (Show Source):
You can put this solution on YOUR website! I am an instructor at a high school and just gave a fifty item multiple choice exam (a,b,c,d). Five students who sit together at a table got the same 8 of the 50 questions wrong. What is the probability of that happening? I want to be able to support the fact that I believe they cheated. Thanks!
---
The probability I give the same answer as you on one question is 1/2
The probability that 6 others give the same answer is (1/2)^6
---
The probability 8 of us give the same answer is (1/2)^7
----
The probability that happens on 8 questions is (1/2)^7^8 = (1/2)^56
----
BUT, if we assume the 8 questions could hardly be answered incorrectly
by anyone taking your class, the probability does not change, but the
reality of the situation would force us to reasses our suspicion.
============================
In other words the theoretical probability does not always tell the
whole story about events. It only tells us something about RANDOM
events.
Question: What is the probability your car will follow some particular
car at a particular red light tomorrow morning? Small, right?
But what is the probability you will follow some car? Hugh, right?
------
Recommend: Look beyond the probabilities.
Cheers,
Stan H.
|
Probability-and-statistics/575430: Assume that a sample is drawn and z(α/2) = 1.65 and σ = 35. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?
(B) Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
(C) What happens to the Maximum Error of Estimate as the sample size gets larger?
(D) What effect does the answer to C above have to the size of the confidence interval?
1 solutions
Answer 369513 by stanbon(57219) on 2012-02-20 21:47:01 (Show Source):
You can put this solution on YOUR website!Assume that a sample is drawn and z(α/2) = 1.65 and σ = 35. Answer the following questions:
(A) If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?
n = [z*s/ME]^2
n = [1.65*35/0.05]^2 = 1155^2 = 1,334,025
-----------------------------------------------------
(B) Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
400 = [1.65*35/ME]^2
[1.65*35/ME = 20
ME = 1.65*35/20
ME = 2.89
------------------------------------------------------
(C) What happens to the Maximum Error of Estimate as the sample size gets larger?
ME and n are inversely related.
As sample size increases the Maximum Error decreases.
-------------------------------------------------------
(D) What effect does the answer to C above have to the size of the confidence interval?
The confidence interval is ALWAYS 2 times ME.
If n increases ME decreases and the CI becomes smaller.
============================================================
Cheers,
Stan H.
============
|
Probability-and-statistics/575508: An urn contains 8 balls identical in every respect except color. There are
4 blue balls, 3 red ones and 1 white one. If you draw two balls without replacing the first one, what is the probability that the first ball is red and the second is white?
1 solutions
Answer 369505 by stanbon(57219) on 2012-02-20 21:28:59 (Show Source):
You can put this solution on YOUR website!4 blue balls, 3 red ones and 1 white one. If you draw two balls without replacing the first one, what is the probability that the first ball is red and the second is white?
-------------
# of ways to draw red and then white: 3*1 = 3
---
# of random pairs: 8C2 = 8*7/1*2 = 28
---
P(red/white) = 3/28
=============================
Cheers,
Stan h.
|
Probability-and-statistics/575509: Student Life did a survey of students in which they asked if the person is
a part-time student or a full-time student. They also asked if the person
had voted in the most recent student election. The results follow:
Part-time Student Full-time Student Row Total
Voted 15 20 35
Did not vote 25 30 55
Column Total 40 50 90
If a student is selected at random from this group of 90 students, find
the probability that :
a) The student voted in the most recent election.
b) The student voted in the most recent election, given that the
student is a part-time student.
c) The student voted in the most recent election and the student
is a part-time student
1 solutions
Answer 369501 by stanbon(57219) on 2012-02-20 21:20:49 (Show Source):
You can put this solution on YOUR website!Student Life did a survey of students in which they asked if the person is
a part-time student or a full-time student. They also asked if the person
had voted in the most recent student election. The results follow:
..............Part-time Student Full-time Student Row Total
Voted 15 20 35
Did not vote 25 30 55
Column Total 40 50 90
If a student is selected at random from this group of 90 students, find
the probability that :
a) The student voted in the most recent election::: 35/90
-----------------------------------
b) The student voted in the most recent election, given that the
student is a part-time student::: 15/40
-----------------------------------
c) The student voted in the most recent election and the student
is a part-time student ::: 15/90
==========================================
Cheers,
Stan H.
==========================================
|
Linear-equations/575507: 1) write the equation in slope intercept form (solved for y), when possible. Through (6,-7) parallel to the y-axis
2) write the equation in slope intercept form (solved for y), when possible. Through (-1,-6) perpendicular to the y-axis
3) Find an equation of the line with the given slope that passes through a given point. write the equation Ax+By=C .... m= -1, (-5,-9)
1 solutions
Answer 369498 by stanbon(57219) on 2012-02-20 21:11:05 (Show Source):
You can put this solution on YOUR website!2) write the equation in slope intercept form (solved for y), when possible. Through (-1,-6) perpendicular to the y-axis
Plot the point and draw the line perpendicular to the y-axis.
It passes thru all the points where y = -6.
Equation: y = -6
==============================
3) Find an equation of the line with the given slope that passes through a given point. write the equation Ax+By=C .... m= -1, (-5,-9)
Use the form y = mx+b
-9 = -1*-5 + b
b = -14
----
Equation: y = -x-14
----
Change the form:
x + y = -14
===========================
Cheers,
Stan H.
|
Travel_Word_Problems/575504: write the equation in slope intercept form (solved for y), when possible. Through (6,-7) parallel to the y-axis
1 solutions
Answer 369496 by stanbon(57219) on 2012-02-20 21:01:27 (Show Source):
You can put this solution on YOUR website!write the equation in slope intercept form (solved for y), when possible. Through (6,-7) parallel to the y-axis
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Plot the point.
Draw a line thru it that is parallel to the y-axis.
Do you see that it passes thru all the points where
x = 6.
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Equation: x = 6
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Cheers,
Stan H.
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Probability-and-statistics/575291: Show the null and alternative hypothesis that you would use to test against the assumption that people drink 3 cups of coffee on the average
1 solutions
Answer 369461 by stanbon(57219) on 2012-02-20 16:29:59 (Show Source):
You can put this solution on YOUR website!Show the null and alternative hypothesis that you would use to test against the assumption that people drink 3 cups of coffee on the average
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Ho: u = 3
Ha: u # 3
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Cheers,
Stan H.
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Probability-and-statistics/575304: Find the probability that when you draw a single card from a well shuffled standard deck of cards, you choose an ace or a club.
Thank you
1 solutions
Answer 369458 by stanbon(57219) on 2012-02-20 16:27:14 (Show Source):
You can put this solution on YOUR website!Find the probability that when you draw a single card from a well shuffled standard deck of cards, you choose an ace or a club.
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# of ways to pick ace or club = 4 + 13 - 1 = 16
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P(pick ace or club) = 16/52 = 4/13
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Cheers,
Stan H.
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Probability-and-statistics/575325: A jar contains 5 red, 3 green, 2 purple and 4 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a purple and then a red marble?
1 solutions
Answer 369457 by stanbon(57219) on 2012-02-20 16:25:06 (Show Source):
You can put this solution on YOUR website!A jar contains 5 red, 3 green, 2 purple and 4 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a purple and then a red marble?
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P(purple) = 2/14
P(red after purple) = 5/13
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P(purple and red) = (2/14)(5/13) = 5/91
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Cheers,
Stan H.
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Probability-and-statistics/575366: A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.
(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it.
1 solutions
Answer 369454 by stanbon(57219) on 2012-02-20 16:22:26 (Show Source):
You can put this solution on YOUR website!A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.
(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.
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p-hat = 45/600 = 0.075
ME = 2.5758*sqrt[0.075*0.9250/600] = 0.0277
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99%CI: 0.075-0.0277 < p < 0.075+0.0277
99%CI: 0.0473 < p < 0.1027
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(b) Interpret this confidence interval and write a sentence that explains it.
We can have 99% confidence that p is between 0.0473 and 0.1027
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Cheers,
Stan H.
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Linear-equations/575364: : WRITE THE SLOPE-INTERCEPT FORM OF THE EQUATION OF THE LINE PERPENDICULAR TO Y=X-2 CONTAINING (3,5)
1 solutions
Answer 369452 by stanbon(57219) on 2012-02-20 16:16:09 (Show Source):
You can put this solution on YOUR website!WRITE THE SLOPE-INTERCEPT FORM OF THE EQUATION OF THE LINE PERPENDICULAR TO
Y = X-2 CONTAINING (3,5)
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The given line has slope = 1.
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Any line perpendicular to y = x-2 must have slope = -1
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Equation Form:
y = mx + b
5 = -1*3 + b
b = 8
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Equation: y = -x+8
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Cheers,
Stan H.
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Geometry_Word_Problems/575363: You are tiling a kitchen floor that is 10ft wide by 4yd long. How many square yards of tile do you need?
1 solutions
Answer 369451 by stanbon(57219) on 2012-02-20 16:12:02 (Show Source):
You can put this solution on YOUR website!You are tiling a kitchen floor that is 10ft wide by 4yd long. How many square yards of tile do you need?
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A square yard is 27 sq. ft.
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Area = 10'*12' = 120 sq. ft.
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Area = 120 sq.ft/27 sq.ft = 4.44 sq yds
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Cheers,
Stan H.
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Triangles/575144: in a 30-60-90 triangle, what is the ratio of the length of the hypotenuse to the shorter leg?
1 solutions
Answer 369410 by stanbon(57219) on 2012-02-20 08:04:57 (Show Source):
You can put this solution on YOUR website!in a 30-60-90 triangle, what is the ratio of the length of the hypotenuse to the shorter leg?
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The side opposite the 30 degree angle is 1/2 the hypotenuse.
Ratio of hypotenuse to shorter leg is 2:1
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Cheers,
Stan H.
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Age_Word_Problems/575149: When Ricky was 10 years old, his father was 45.How many years must pass for Ricky to be 5 years older than 1/5 as old as his father?
1 solutions
Answer 369404 by stanbon(57219) on 2012-02-20 07:37:44 (Show Source):
You can put this solution on YOUR website!When Ricky was 10 years old, his father was 45.How many years must pass for Ricky to be 5 years older than 1/5 as old as his father?
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(10+x) = (1/5)(45+x)+5
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5 + x = (1/5)(45+x)
25+5x = 45+x
4x = 20
x = 5
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In 5 years dad will be 50
In 5 years son will be 15
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Cheers,
Stan H.
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Cheers,
Stan H.
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Probability-and-statistics/575156: kindly help me answer this, if two people are selected at random, find the probability that both were born in August.
1 solutions
Answer 369401 by stanbon(57219) on 2012-02-20 07:28:23 (Show Source):
You can put this solution on YOUR website!kindly help me answer this, if two people are selected at random, find the probability that both were born in August.
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The 1st can be born in any month.
The 2nd has a probability of 1/12 of being born in the same month.
Cheers,
Stan H.
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Probability-and-statistics/575154: 4. The amounts of money requested small business loan applications at GetBuckets Fantake Commercial Savings Bank follows the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. What is the probability that the amount requested is $80,000 or more?
a. .3500
b. .3085
c. .2902
d. .5987
5. Using Problem #4, what is the probability the amount requested is between $65,000 and $80,000?
a. .4500
b. .2902
c. .5987
d. None of the above
1 solutions
Answer 369400 by stanbon(57219) on 2012-02-20 07:26:35 (Show Source):
You can put this solution on YOUR website!4. The amounts of money requested small business loan applications at GetBuckets Fantake Commercial Savings Bank follows the normal distribution, with a mean of $70,000 and a standard deviation of $20,000. What is the probability that the amount requested is $80,000 or more?
a. .3500
b. .3085
c. .2902
d. .5987
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normalcdf(80000,10^10,70000,20000) = 0.3085
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5. Using Problem #4, what is the probability the amount requested is between $65,000 and $80,000?
a. .4500
b. .2902
c. .5987
d. None of the above
normalcdf(65000,80000,70000,20000) = 0.2902
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Cheers,
Stan H.
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