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Recent problems solved by 'stanbon'
stanbon answered: 57151 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 , 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, >>NextMixture_Word_Problems/276530: How many ounces of a 20% saline solution must be added to 40 ounces of a 10% solution to produce a 16% solution?
1 solutions
Answer 201486 by stanbon(57219)   on 2010-03-03 08:56:10 (Show Source):
You can put this solution on YOUR website!How many ounces of a 20% saline solution must be added to 40 ounces of a 10% solution to produce a 16% solution?
---------------------------------------
One-variable solution:
Equation:
0.20x + 0.10*40 = 0.16(x+40)
Multiply thru by 100 to get:
20x + 10*40 = 16x + 16*40
4x = 6*40
x = 6*10
x = 60 oz (amt of 20% solution needed in for the mixture)
=============================================================
Cheers,
Stan H.
|
Probability-and-statistics/276476: a NEW CAR SALESMEN KNOWS THAT HE SELLS CARS TO ONE CUSTOMER OUT OF TEN WHO ENTERS THE SHOW ROOM.WHAT IS THE PROBABILITY THAT HE WILL SELL A CAR TO EXACTLY 2 OF THE NEXT 3 CUSTOMERS.IS IT:
1)0.027
2)0.973
3)0.000
4)0.090
5)0.901
1 solutions
Answer 201480 by stanbon(57219) on 2010-03-03 08:39:49 (Show Source):
You can put this solution on YOUR website!a NEW CAR SALESMEN KNOWS THAT HE SELLS CARS TO ONE CUSTOMER OUT OF TEN WHO ENTERS THE SHOW ROOM.WHAT IS THE PROBABILITY THAT HE WILL SELL A CAR TO EXACTLY 2 OF THE NEXT 3 CUSTOMERS.IS IT:
-----
Binomial Problem with n=3 ; p = 0.1 ; x = 2
P(x=2) = 3C2(0.1)^2*(0.9) = 3*0.01*0.9 = 0.027
=============
Cheers,
Stan H.
=============
1)0.027
2)0.973
3)0.000
4)0.090
5)0.901
|
Probability-and-statistics/276489: Please help me solve this problem
A Family composed of a father a mother and 3 kids are to be arranged in a row to have their picture taken.
a) In how many ways can this be done?
b) In how many ways can this be done if the father is to be on one end of the picture and the mother on the other?
1 solutions
Answer 201478 by stanbon(57219) on 2010-03-03 08:34:41 (Show Source):
You can put this solution on YOUR website!A Family composed of a father a mother and 3 kids are to be arranged in a row to have their picture taken.
a) In how many ways can this be done?
Ans: 5P5 = 5!/(5-5)! = 5!/0! = 5! = 120
-----------------------------------------------------
b) In how many ways can this be done if the father is to be on one end of the picture and the mother on the other?
Arrange father and mother: 2 ways
Arrange the three children: 3! = 6
---------------
Total arrangements = 2*6 = 12
==================================
Cheers,
Stan H.
|
Age_Word_Problems/276430: Shelly is three years older than Michele. Four years ago the sum of their ages was 67. Find the age of the person now. Can you give me a basic formula to solving most Age Word Problems.
1 solutions
Answer 201446 by stanbon(57219) on 2010-03-02 22:42:58 (Show Source):
You can put this solution on YOUR website!Shelly is three years older than Michele. Four years ago the sum of their ages was 67. Find the age of the person now.
----------------------
Equation:
S = M+3
(S-4)+(M-4) = 67
----------------------
Modify the 2nd equation:
S + M = 67+8 = 75
---
Substitute for "S" and solve for "M":
M+3 + M = 75
2M = 72
M = 36 (Michele's age now)
----
Since S = M+3, S = 39 (Shelly's age now)
=============================================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/276427: Vong grilled 21 burgers at a block party. He grilled the same number of pounds of turkey burgers as hamburgers. Each turkey burger weighed 1/4 pound and each hamburger weighed 1/3 pound. How many of each did Vong grill?
1 solutions
Answer 201444 by stanbon(57219) on 2010-03-02 22:35:49 (Show Source):
You can put this solution on YOUR website!Vong grilled 21 burgers at a block party. He grilled the same number of pounds of turkey burgers as hamburgers. Each turkey burger weighed 1/4 pound and each hamburger weighed 1/3 pound. How many of each did Vong grill?
---------------------
Quantity Eq: t + h = 21
Weight Eq::: (1/4)t - (1/3)h = 0
---------------------------------------
Modify the equations:
3t - 4h = 0
3t + 3h = 3*21
-------------------
Subtract 1st from the 2nd:
7h = 3*21
h = 9 (# of turkey burgers grilled)
------------------
Since t + h = 21, h = 12 (# of hamburgers grilled)
=======================================================
Cheers,
Stan H.
=======================================================
|
Probability-and-statistics/276120: many radio ststions in the united states have call letters that begin with a W or a K and have four letters.
how many arrangements of four leeters are possible as call letter?
what is the probility of having call letters KIDS?
1 solutions
Answer 201442 by stanbon(57219) on 2010-03-02 22:27:47 (Show Source):
You can put this solution on YOUR website!many radio ststions in the united states have call letters that begin with a W or a K and have four letters.
how many arrangements of four leeters are possible as call letter?
---
1st letter 2 ways
2nd letter 26 ways
3rd letter 26 ways
4th letter 26 ways
-------------------------------
Total # of possible arrangements: 2*26^3 = 35152
-----
what is the probility of having call letters KIDS?
Ans: 1/35152
================================
Cheers,
Stan H.
|
Graphs/276409: If the graph of f is decreasin on [0,infinity)the what can be said about the graph of y=f(-x)+1? The graph of y=-f(x)-1?
1 solutions
Answer 201441 by stanbon(57219) on 2010-03-02 22:21:09 (Show Source):
You can put this solution on YOUR website!If the graph of f is decreasing on [0,infinity)the what can be said about the graph of y=f(-x)+1? The graph of y=-f(x)-1?
-----------------------------------------
f(-x) + 1 is a reflection in the y-axis and a +1 vertical shift.
---
If f(x) is decreasing to the right of the y-axis
f(-x) will be increasing to the left of the y-axis.
The +1 will move all points 1 unit up but the function
will still be increasing on (-infinity,0]
--------------------------------------------------------
-f(x)-1 is a reflection in the x-axis followed by a vertical shift down one
If f(x) is decreasing to the right of the y-axis
-f(x) will be increasing to the right of the y-axis.
The -1 will move all points 1 unit down but the function
will still be increasing on [0,+infinity)
===============================================
Cheers,
Stan H.
|
Probability-and-statistics/276406: Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B).
7/24 is the answer but I would really love to know why. This question is worded in a very confusing manner.
1 solutions
Answer 201439 by stanbon(57219) on 2010-03-02 21:56:40 (Show Source):
You can put this solution on YOUR website!Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B).
7/24 is the answer but I would really love to know why
----
General Formula:
P(A or B) = P(A) + p(B) - P(A and B)
---
Substitute:
1/3 = (1/6) + P(B) - 1/8
----
Multiply thru by 24 to get:
8 = 4 + 24P(B) - 3
24P(B) = 7
P(B) = 7/24
================================
Cheers,
Stan H.
================================
|
Probability-and-statistics/276370: A coin is flipped 3 times and heads (H) or tails (T) are recorded.
a. List all three elements in the sample area.
b. List the elements in the event "at least two heads appear."
c. Find the probability that the event in part (b) occurs.
1 solutions
Answer 201438 by stanbon(57219) on 2010-03-02 21:52:56 (Show Source):
You can put this solution on YOUR website!A coin is flipped 3 times and heads (H) or tails (T) are recorded.
a. List all three elements in the sample area.
3 heads: hhh
1 head:: htt, tht,tth
2 heads: thh,hth,hht
0 heads: ttt
-----------------------------
b. List the elements in the event "at least two heads appear."
hhh,thh,hth,hht
-----------------------------------------
c. Find the probability that the event in part (b) occurs.
# of ways to succeed: 4
# of possible outcomes: 8
Probability: 4/8 = 1/2
==============================
Cheers,
Stan H.
|
Probability-and-statistics/276399: You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
The answer is 244,140,625 but why?
1 solutions
Answer 201436 by stanbon(57219) on 2010-03-02 21:46:51 (Show Source):
You can put this solution on YOUR website!You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
---
Each question has 5 possible choices for an answer>
1st question: 5 ways
2nd question: 5 ways
.......
12th question: 5 ways
----
Total # of possible answers 5*5*5...*5*5 = 5^12 = 244,140,625
-----
Cheers,
Stan H.
=========================
The answer is 244,140,625 but why?
|
Probability-and-statistics/276388: A company claims to have invented a hand-held sensor that can detect the presence of explosives inside a closed container. Law enforcement and security agencies are very interested in purchasing several of the devices if they are shown to perform effectively. An independent laboratory arranged a test. They placed four empty boxes in the corners of an otherwise empty room. For each trial they put a small quantity of an explosive in one of the boxes selected at random. The company's technician then entered the room and used the sensor to try to determine which of the four boxes contained the explosive. The experiment consisted of 50 trials, and the technician was successful in finding the explosive 16 times. Does this indicate that the device is effective in sensing the presence of explosives?
1. Test an appropriate hypothesis and state your conclusion.
2. Was your test one-tail lower, or two tail? Explain why you chose that kind of test in this situation.
3. Explain what your P-value means in this context.
1 solutions
Answer 201433 by stanbon(57219) on 2010-03-02 21:42:10 (Show Source):
You can put this solution on YOUR website!The company's technician then entered the room and used the sensor to try to determine which of the four boxes contained the explosive. The experiment consisted of 50 trials, and the technician was successful in finding the explosive 16 times. Does this indicate that the device is effective in sensing the presence of explosives?
1. Test an appropriate hypothesis and state your conclusion.
Ho: p >= 0.5
Ha: p < 0.5
-------------
2. Was your test one-tail lower, or two tail? Explain why you chose that kind of test in this situation.
--
One-tail lower because we are assuming a detection level higher than random.
We do not want to have a rejection interval where p-hat is a high number,
only where p-hat is a lower number.
--------------------------------------------
3. Explain what your P-value means in this context.
The p-value will be the probability that test results could give
stronger evidence for rejecting Ho.
================================================
Cheers,
Stan H.
|
Probability-and-statistics/276372: . In a British study around 1925, a group of 649 men with lung cancer were surveyed. A control group of the same size was established from a set of men who did not have lung cancer. The groups were matched according to ethnicity, age, and socioeconomic status. The statistics from the survey follow.
What type/Lung Cancer Cases/Controls/Totals
Smokers/647/622/1269
Non-smokers/2/27/29
a. What is the proportion of smoking in the group that has lung cancer in the study?
b. What is the proportion of smoking in the control group?
c. If one person is chosen at random from each of the two groups, what is the probability that each person chosen has cancer?
d. Do you think that this data presents a strong association between lung cancer and smoking? Explain your answer.
e. Do you think that this evidence is conclusive that smoking causes lung cancer?
1 solutions
Answer 201426 by stanbon(57219) on 2010-03-02 21:20:41 (Show Source):
You can put this solution on YOUR website!In a British study around 1925, a group of 649 men with lung cancer were surveyed. A control group of the same size was established from a set of men who did not have lung cancer. The groups were matched according to ethnicity, age, and socioeconomic status. The statistics from the survey follow.
What type/Lung Cancer Cases/Controls/Totals
Smokers:::::::/647:::::::::::/622::::/1269
Non-smokers::::/2::::::::::::/27:::::/29
a. What is the proportion of smoking in the group that has lung cancer in the study? (647/649
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b. What is the proportion of smoking in the control group? 622/649
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c. If one person is chosen at random from each of the two groups, what is the probability that each person chosen has cancer?
Smoker Group: 647/1269
non-smok grp: 2/29
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d. Do you think that this data presents a strong association between lung cancer and smoking? Explain your answer.
===
e. Do you think that this evidence is conclusive that smoking causes lung cancer?
Comment: d and e are discussion questions. I'll leave them up to you.
===============================
Cheers,
Stan H.
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Probability-and-statistics/276369: A student observes the following spinner and claims that the color red has the highest probability of appearing, since there are two red areas on the spinner. What is your reply to the student?
The picture of the spinner shows 1/2 green, 1/4 blue, and 2 (1/8 sections) red
1 solutions
Answer 201424 by stanbon(57219) on 2010-03-02 21:03:16 (Show Source):
You can put this solution on YOUR website!A student observes the following spinner and claims that the color red has the highest probability of appearing, since there are two red areas on the spinner. What is your reply to the student?
The picture of the spinner shows 1/2 green, 1/4 blue, and 2 (1/8 sections) red
--------------------------
It appears there are 8 sections on the spinner:
4 are green
2 are blue
2 are red
----------------------
If the above is true, the highest probability is the color green.
---
Red has two sections but not the highest area and therefore not
the highest probability.
===================================
cheers,
Stan H.
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Probability-and-statistics/276206: On average, 40 percent of US beer drinkers order light beer.
a) What is the probability that none of the next eight customers who order beer will order light beer?
b) That one customer will?
c) Two customers?
d) Fewer than three?
1 solutions
Answer 201421 by stanbon(57219) on 2010-03-02 20:55:00 (Show Source):
You can put this solution on YOUR website!On average, 40 percent of US beer drinkers order light beer.
Each is a Binomial problem with p = 0.40
-----------------------------------
a) What is the probability that none of the next eight customers who order beer will order light beer?
n = 8 ; x = 0
P(x=0) = 8C0(0.4)^0*(0.6)^8 = 0.0168
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b) That one customer will?
P(x=1) = 8C1(0.4)*(0.6)^7
---------------------------------
Same procedure as above.
c) Two customers?
--------------------------
d) Fewer than three?
P(0<= x <=2) = binomcdf(8,0.4,2) = 0.3154...
================================================
Cheers,
Stan H.
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Probability-and-statistics/276336: Of 1937 people who came into a blood bank to give blood, 679 had high blood pressure. Estimate the probability that the next person who comes in will also have high blood pressure.
Thanks
1 solutions
Answer 201414 by stanbon(57219) on 2010-03-02 20:30:21 (Show Source):
You can put this solution on YOUR website!Of 1937 people who came into a blood bank to give blood, 679 had high blood pressure. Estimate the probability that the next person who comes in will also have high blood pressure.
--------------
Ans: (679/1937)
-------------------
Cheers,
Stan H.
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Probability-and-statistics/276339: A binomial distribution has n=1580 and p=0.798. Find the mean of this distribution to the nearest tenth. Find the variance and standard deviation of this distribution to the nearest hundredth. Find the minimum and maximum usual values of mu +- 2 r
1 solutions
Answer 201413 by stanbon(57219) on 2010-03-02 20:28:08 (Show Source):
You can put this solution on YOUR website!A binomial distribution has n=1580 and p=0.798. Find the mean of this distribution to the nearest tenth. Find the variance and standard deviation of this distribution to the nearest hundredth. Find the minimum and maximum usual values of mu +- 2 r
------
mean = np =
variance = npq =
std = sqrt(npq) =
----
u-2std = np - 2sqrt(npq) =
u+2std = np + 2sqrt(npq) =
================================
Cheers,
Stan H.
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Proportions/276142: I am trying to figure out the solution to the question
95 is 90% of what number.
Do I divide or multiply
95* 90%=85.5
95/90%=105.56
I get confused
1 solutions
Answer 201297 by stanbon(57219) on 2010-03-02 13:04:52 (Show Source):
You can put this solution on YOUR website!I am trying to figure out the solution to the question
95 is 90% of what number.
----
Let "x" be the number.
----
Equation:
90% of x = 95
0.90x = 95
x = 95/0.9
x = 105.56
====================
cheers,
Stan H.
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Probability-and-statistics/276139: Bob is trying to borrow $1000 from friends. One of every 3 friends asked responds that their money is tied up. Of his friends with money not tied up, 2 out of 5 inform him quickly that they won't lend him money. Of the remainder, 1 out 2 won't lend him money on general principles. If Bob called 60 friends, how many might lend him money?
1 solutions
Answer 201296 by stanbon(57219) on 2010-03-02 13:01:47 (Show Source):
You can put this solution on YOUR website!Bob is trying to borrow $1000 from friends. One of every 3 friends asked responds that their money is tied up. Of his friends with money not tied up, 2 out of 5 inform him quickly that they won't lend him money. Of the remainder, 1 out 2 won't lend him money on general principles. If Bob called 60 friends, how many might lend him money?
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1 of every 3 = 20::::::40 remain
2 of 5 of the 40 remaining = 16:::: 24 remain
1 of 2 of the remaining = 12::::12 will lend him money
===================================================
Cheers,
Stan H.
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Probability-and-statistics/276086: We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value for the game?
1 solutions
Answer 201293 by stanbon(57219) on 2010-03-02 12:57:07 (Show Source):
You can put this solution on YOUR website!We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value for the game?
------------------------------------------
Random "Values" to the player: -30 , 2, 3, 4, 5, 6 , 8, 9, 10, 11, 12
P(get sum of 2) = 1/36
P(get sum of 3) = 2/36
P(get sum of 4) = 3/36
P(get sum of 5) = 4/36
P(get sum of 6) = 5/36
P(get sum of 7) = 6/36
P(get sum of 8) = 5/36
P(get sum of 9) = 4/36
P(get sum of 10)= 3/36
P(get sum of 11) = 2/36
P(get sum of 12) + 1/36
---------------------------------
Procedure:
E(x) = (2+12)(1/36) + (3+11)(2/36) + (4+10)(3/36) + (5+9)(4/36) + (6+8)(5/36)
-30(6/36)
----
E(x) = (14/36)[(1+2+3+4+5)]-30(6/36)] = (7/18)(15)-5 = +83 cents
============
Cheers,
Stan H.
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Quadratic_Equations/276067: What is the greatest common factor of the terms 48s^5t^3u^2 and 40s^3tu^4?
1 solutions
Answer 201274 by stanbon(57219) on 2010-03-02 11:04:55 (Show Source):
You can put this solution on YOUR website!What is the greatest common factor of the terms 48s^5t^3u^2 and 40s^3tu^4?
---
gcf of 48 and 40 = 8
gcf of s^5 and s^3 is s^3
gcf of t^3 and t is t
gcf of u^2 and u^4 is u^2
--------------------------------
GCF for your problem pair: 8s^3*t*u^2
================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/276068: Solve the problem. The difference between two numbers is 4. Two times the smaller number minus four times the larger is -28. What are the numbers?
1 solutions
Answer 201273 by stanbon(57219) on 2010-03-02 11:01:40 (Show Source):
You can put this solution on YOUR website!Solve the problem. The difference between two numbers is 4. Two times the smaller number minus four times the larger is -28. What are the numbers?
-----------------------
x - y = 4
2y - 4x = -28
-----------------------------
Rearrange:
-2y + 2x = 8
2y - 4x = -28
------------------------
Add and solve for "x":
-2x = -20
x = 10
-----
Substitute and solve for "y":
10-y = 4
y = 6
-------------------
cheers,
Stan H.
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Travel_Word_Problems/276065: At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.?
1 solutions
Answer 201272 by stanbon(57219) on 2010-03-02 10:58:43 (Show Source):
You can put this solution on YOUR website!At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.?
--------------------
Slower Car DATA:
distance = x ; time = 3 hrs ; rate = d/t = x/3 hrs
-------------------------
Faster Car DATA:
distance = (240-x) ; time = 3 hrs ; rate = d/t = (240-x)/3
-----------------------------
Equation:
faster rate - slower rate = 10 mph
(240-x)/3 - x/3 = 10 mph
240-x - x = 30
-2x = -210
x = 105 miles
----
slower car rate = 105/3 = 35 mph
faster car rate = 35+10 = 45 mph
===================================
Cheers,
Stan H.
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Radicals/276064: 2√2 + 6√2 =
Simplify by collecting like radical terms, if possible. Type an exact answer using radicals as needed
1 solutions
Answer 201269 by stanbon(57219) on 2010-03-02 10:51:38 (Show Source):
You can put this solution on YOUR website!2√2 + 6√2 =
Simplify by collecting like radical terms, if possible. Type an exact answer using radicals as needed
-------
= 8sqrt(2)
================
Cheers,
Stan H.
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Probability-and-statistics/275990: You are responsible for reliability of the electronic product that your company produces.
You decide to measure the time between equipment malfunctions over a one-year period. Over that time you measured 40 electronic products. You made 850 observations with a mean time between equipment failures of 550.35 hours, and a sample standard deviation of 207 hours.
Your company supplies the electronic product to another company as a component to their product. You guarantee an average time between malfunctions of 600 or more hours.
Calculate a 99% confidence interval estimate for the mean time between malfunctions for all electronics of this type then interpret the results to assess whether your company will have a problem with this guarantee. Explain your reasoning?
1 solutions
Answer 201267 by stanbon(57219) on 2010-03-02 10:50:26 (Show Source):
You can put this solution on YOUR website!You are responsible for reliability of the electronic product that your company produces.
You decide to measure the time between equipment malfunctions over a one-year period. Over that time you measured 40 electronic products. You made 850 observations with a mean time between equipment failures of 550.35 hours, and a sample standard deviation of 207 hours.
Your company supplies the electronic product to another company as a component to their product. You guarantee an average time between malfunctions of 600 or more hours.
Calculate a 99% confidence interval estimate for the mean time between malfunctions for all electronics of this type then interpret the results to assess whether your company will have a problem with this guarantee. Explain your reasoning?
---
sample mean = 550.35
standard error = E = invNorm(0.995)*207/sqrt(850) = 18.29
---------------------
99% CI: 550.35-18.29 < u < 550.35+18.29
99% CI: 532.06 < u < 568.64
============================
For your component your guarantee it too high.
===================================
Cheers,
Stan H.
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Probability-and-statistics/275991: You have measured the temperature of a large number of patients at a local clinic.
You find the 95% confidence interval to be 96.7 and 99.1.
In another sample of a large number of patients a mistake was made in an entry.
a. If instead of an entry of 98.6 an error was made and entered as 9.86, what is the effect on the confidence interval? Explain.
b. If instead of an entry of 98.6 an error was made and entered as 986, what is the effect on the confidence interval? Explain.
c. What tips you to a confidence interval that needs investigation for error?
1 solutions
Answer 201264 by stanbon(57219) on 2010-03-02 10:38:50 (Show Source):
You can put this solution on YOUR website!You have measured the temperature of a large number of patients at a local clinic.
You find the 95% confidence interval to be 96.7 and 99.1.
In another sample of a large number of patients a mistake was made in an entry.
a. If instead of an entry of 98.6 an error was made and entered as 9.86, what is the effect on the confidence interval? Explain.
The sample mean (x-bar) will be lower so the confidence
interval will slide to the left.
b. If instead of an entry of 98.6 an error was made and entered as 986, what is the effect on the confidence interval? Explain.
The sample mean (x-bar) will be higher so the CI will slide to the right.
c. What tips you to a confidence interval that needs investigation for error?
The range of the CI seems to be out of keeping with the range of the data.
=============================================================================
Cheers,
Stan H.
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Probability-and-statistics/276046: in one city, the probability that a person will pass his or her driving test on the first attempt is 0.61. 11 people are selected at random from among those taking their driving test for the first time. What is the probability that among these 11 people, the number passing the test is between 2 and 4 inclusive?
1 solutions
Answer 201262 by stanbon(57219) on 2010-03-02 10:31:10 (Show Source):
You can put this solution on YOUR website! in one city, the probability that a person will pass his or her driving test on the first attempt is 0.61. 11 people are selected at random from among those taking their driving test for the first time. What is the probability that among these 11 people, the number passing the test is between 2 and 4 inclusive?
---------------------------------------------------------
Binomial Problem with n = 11 ; p = 0.61 ; 2<=x<=4
-----
P(2<=x<=4) = binomcdf(11,0.61,4)-binomcdf(11,0.61,1) = 0.0870
===================
Cheers,
Stan H.
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Probability-and-statistics/275992: As the new city planner for a developing community you need to project a budget for garbage trucks. To support your numbers you will use an estimate of the mean weight of garbage discarded weekly by household.
a. Find the sample size necessary to estimate the mean if you want to be 90% confident that the sample mean is within 2 pounds of the true population mean. A sample of 62 households produced a standard deviation = 12.46 pounds
Try it again at a 95% and a 99% confidence and indicate the change in the sample size and why you think this is so.
b. Give an example from your workplace of a problem that requires you to determine a sample size.
1 solutions
Answer 201236 by stanbon(57219) on 2010-03-02 08:57:28 (Show Source):
You can put this solution on YOUR website!As the new city planner for a developing community you need to project a budget for garbage trucks. To support your numbers you will use an estimate of the mean weight of garbage discarded weekly by household.
a. Find the sample size necessary to estimate the mean if you want to be 90% confident that the sample mean is within 2 pounds of the true population mean. A sample of 62 households produced a standard deviation = 12.46 pounds
----
n = [z*s/E]^2
n = [invNorm(0.95]*(12.46/(sqrt(62))/2]^2
---
n = [1.96*24.92/sqrt(62)]^2
n = 38.48
Round up to n = 39
======================================
Try it again at a 95%
Change the z-value to invNorm(0.975)
---
and a 99% confidence
Change the z-value to invNorm(0.995)
-----
and indicate the change in the sample size and why you think this is so.
More confidence and sample size are directly related.
===========================================================
b. Give an example from your workplace of a problem that requires you to determine a sample size.
I'll leave that to you.
Cheers,
Stan H.
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