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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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43110..43139 , 43140..43169 , 43170..43199 , 43200..43229 , 43230..43259 , 43260..43289 , 43290..43319 , 43320..43349 , 43350..43379 , 43380..43409 , 43410..43439 , 43440..43469 , 43470..43499 , 43500..43529 , 43530..43559 , 43560..43589 , 43590..43619 , 43620..43649 , 43650..43679 , 43680..43709 , 43710..43739 , 43740..43769 , 43770..43799 , 43800..43829 , 43830..43859 , 43860..43889 , 43890..43919 , 43920..43949 , 43950..43979 , 43980..44009 , 44010..44039 , 44040..44069 , 44070..44099 , 44100..44129 , 44130..44159 , 44160..44189 , 44190..44219 , 44220..44249 , 44250..44279 , 44280..44309 , 44310..44339 , 44340..44369 , 44370..44399 , 44400..44429 , 44430..44459 , 44460..44489 , 44490..44519 , 44520..44549 , 44550..44579 , 44580..44609 , 44610..44639 , 44640..44669 , 44670..44699 , 44700..44729 , 44730..44759 , 44760..44789 , 44790..44819 , 44820..44849 , 44850..44879 , 44880..44909 , 44910..44939 , 44940..44969 , 44970..44999 , 45000..45029 , 45030..45059 , 45060..45089 , 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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 , 57180..57209 , 57210..57239, >>NextProbability-and-statistics/568593: On a 10 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
1 solutions
Answer 367045 by stanbon(57290)   on 2012-02-06 16:44:42 (Show Source):
You can put this solution on YOUR website! On a 10 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
------------------------
P(at least one) = 1 - P(none wrong) = 1 - (1/2)^10 = 1 - 1/1024
----
= 1023/1024
==============
Cheers,
Stan H.
==============
|
Probability-and-statistics/568591: A die is rolled twice. Find the probability of the given event.
(a) Getting at least one 3.
1 solutions
Answer 367044 by stanbon(57290) on 2012-02-06 16:40:53 (Show Source):
You can put this solution on YOUR website!A die is rolled twice. Find the probability of the given event.
(a) Getting at least one 3.
-----
P(no 3 in 2) = (5/6)^2
--------
P(at least one 3) = 1- P(no 3's)
= 1 - (5/6)^2
----
= 1 - (25/36)
---
= 11/36
============
Cheers,
Stan H.
===============
|
Probability-and-statistics/568461: A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a B, C or D. Each number must be a 5 or 6. Repetition of digits is permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation
List the sample space.
Determine the exact probability of creating a mini license plate with a B. Give solution exactly in reduced fraction form.
1 solutions
Answer 367020 by stanbon(57290) on 2012-02-06 15:56:42 (Show Source):
You can put this solution on YOUR website!A mini license plate for a toy car must consist of a letter followed by two numbers.
Pattern: LNN
-------------------------
Each letter must be a B, C or D. Each number must be a 5 or 6. Repetition of digits is permitted.
Use the counting principle to determine the number of points in the sample space.
Ans: 3*2*2 = 12
---------------------------------
Construct a tree diagram to represent this situation
List the sample space.
B55,B56,B65,B66,C55,C56,C65,C66,D55,D56,D65,D66
---------------------------------------
Determine the exact probability of creating a mini license plate with a B. Give solution exactly in reduced fraction form.
Ans: 4/12 = 1/3
======================
Cheers,
Stan H.
=====================
-----------------------
|
Probability-and-statistics/568547: A distribution center receives shipment of a product from 3 different factories in quantities of 60, 45, and 25, Three times a product is selected at random without replacement. Find the probability that all three products came from the 3rd factory.
1 solutions
Answer 367016 by stanbon(57290) on 2012-02-06 15:50:50 (Show Source):
You can put this solution on YOUR website!A distribution center receives shipment of a product from 3 different factories in quantities of 60, 45, and 25, Three times a product is selected at random without replacement. Find the probability that all three products came from the 3rd factory.
-----
# of ways to succeed: 25C3 = 2300
--
# of ways to choose 3 randomly: 130C3 = 357760
============
P(3 from 3rd) = 2300/357760
================================
cheers,
Stan H.
|
Probability-and-statistics/568237: The ACT exam math section scores are normally distributed with mean 18 and standard deviation 6. A particular engineering college will only accept high school seniors with ACT math scores in the top 15%. What is the minimum ACT math score that will be accepted?
1 solutions
Answer 367011 by stanbon(57290) on 2012-02-06 15:46:58 (Show Source):
You can put this solution on YOUR website!The ACT exam math section scores are normally distributed with mean 18 and standard deviation 6. A particular engineering college will only accept high school seniors with ACT math scores in the top 15%. What is the minimum ACT math score that will be accepted?
--------------
z-score withe a right tail of 15%: invNorm(0.85) = 1.0364
---
x = zs+u
x = 1.0364*6 + 18
x = 24.22 (minimum scoree accepted)
===============
Cheers,
Stan H.
|
Graphs/568498: 7x+y=6
35x-30=-5y
without graphing answer the following questions about the system.
1. Does the system have one solution, no solution, infinite solution?
2. Is the system inconsistent, are the equations dedendent, or neither?
3. What does the graph look like interesecting lines, one line,Parallel lines?
1 solutions
Answer 366980 by stanbon(57290) on 2012-02-06 14:36:56 (Show Source):
You can put this solution on YOUR website!7x+y=6
35x-30=-5y
---
solve each equation for "y":
y = -7x+6
y = -7x+6
-------------------
without graphing answer the following questions about the system.
1. Does the system have one solution, no solution, infinite solution?
Ans: infinite
---------------------
2. Is the system inconsistent, are the equations dependent, or neither?
Ans: dependent
----------------------
3. What does the graph look like interesecting lines, one line,Parallel lines?
Ans: One line
===================
Cheers,
Stan H.
==============
|
Travel_Word_Problems/568500: If a train travels at 112 mph for 15 minutes, what is the distance traveled?
1 solutions
Answer 366978 by stanbon(57290) on 2012-02-06 14:34:15 (Show Source):
You can put this solution on YOUR website!If a train travels at 112 mph for 15 minutes, what is the distance traveled?
-----
Ans: distance = rate*time
d = 112 mph * (1/4) hours = 28 miles
=========================================
cheers,
Stan H.
|
Expressions-with-variables/568501: I need help for this question:
Define variables and write an equation to model the relationship in each table.
Number of hours. Total Pay
4 $32
6. $48
8. $64
10. $80
Any help would be appreciated! Thank you!
1 solutions
Answer 366975 by stanbon(57290) on 2012-02-06 14:31:55 (Show Source):
You can put this solution on YOUR website!I need help for this question:
Define variables and write an equation to model the relationship in each table.
Number of hours. Total Pay
4 $32
6. $48
8. $64
10. $80
------
Total Pay = 8*(Number of hours)
---
P = 8n
=======================
Cheers,
Stan H.
===========
|
Polynomials-and-rational-expressions/568486: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus sign is throwing me off. I know that the signs to the right of the minus sign change, but I'm having a little trouble with the combining. One of my problems is as follows:
2x-3/x+5-x^2-4x-19/x^2+8x+15
1 solutions
Answer 366973 by stanbon(57290) on 2012-02-06 14:28:36 (Show Source):
You can put this solution on YOUR website!Use parentheses so you can see what you are doing.
-------------------
(2x-3)/(x+5)-(x^2-4x-19)/(x^2+8x+15)
----
Factor:
= (2x-3)/(x+5) - (x^2-4x-19)/[(x+5)(x+3)]
-----------------
LCD = (x+5)(x+3)
-----
Rewrite both factors with denominator = LCD
----
= [(x+3)(2x-3)]/LCD - [x^2-4x-19]/LCD
-------
Combine the numerators over the LCD:
---
= [2x^2+3x-9-x^2+4x+19]/LCD
----------------
Simplify:
= [x^2+7x+10]/LCD
----
Factor:
= [(x+5)(x+2)]/[(x+5)(x+3)]
----
Cancel the common factor:
= (x+2)/(x+3)
=======================
Cheers,
Stan H.
=============
|
Mixture_Word_Problems/568488: How many liters of pure antifreeze (100% solution) must be added to 30 liters of a 15% antifreeze solution to get a 40% antifreeze solution?
1 solutions
Answer 366972 by stanbon(57290) on 2012-02-06 14:19:22 (Show Source):
You can put this solution on YOUR website!How many liters of pure antifreeze (100% solution) must be added to 30 liters of a 15% antifreeze solution to get a 40% antifreeze solution?
---
alcohol + alcohol = alcohol
----
1*x + 0.15*30 = 0.40(x+30)
----
Multiply thru by 100 to get:
100x + 15*30 = 40*x + 40*30
60x = 25*30
x = (1/2)25 = 12.5 liters (amt. of pure antifreeze needed)
============================================================
cheers,
Stan H.
|
Probability-and-statistics/568490: A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.35 of ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.15 .
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number
1 solutions
Answer 366971 by stanbon(57290) on 2012-02-06 14:15:57 (Show Source):
You can put this solution on YOUR website!What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.35 of ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.15 .
----------
n = [zs/E]^2
---
n = [1.96*2.15/0.35]^2 = 145
===================================
cheers,
Stan H.
===============================
|
Polygons/568483: If the measure of each interior angle of a regular polygon is five times the measure of each exterior angle, how many sides does the polygon have ?
1 solutions
Answer 366969 by stanbon(57290) on 2012-02-06 14:10:25 (Show Source):
You can put this solution on YOUR website!If the measure of each interior angle of a regular polygon is five times the measure of each exterior angle, how many sides does the polygon have ?
---
ext + int = 180 degrees
int = 5*ext
--
ext + 5ext = 180
est = 30 degrees
----
sum of the exterior angles is 360
# of exterior = 360/30 = 12
---
# of sides is 12
===================
Cheers,
Stan H.
=============
|
Equations/568472: Find the smallest positive number t such that
e^(sin(t))=5/7
1 solutions
Answer 366968 by stanbon(57290) on 2012-02-06 13:59:31 (Show Source):
You can put this solution on YOUR website!Find the smallest positive number t such that
e^(sin(t))=5/7
-----
Take the natural log of both sides to get:
sin(t) = ln(5/7)
---
sin(t) = -0.3365
---
Take the inverse sin of both sides to get:
t = 200.07 degrees or 3.4848 radians
==================
Cheers,
Stan H.
==================
|
Permutations/568478: If P(A or B) = 0.3, P(A) = 0.7 and P(B) = 0.5, determine
P(A and B).
( 0.90
0.45
0.27
0.15
1 solutions
Answer 366966 by stanbon(57290) on 2012-02-06 13:52:43 (Show Source):
You can put this solution on YOUR website!If P(A or B) = 0.3, P(A) = 0.7 and P(B) = 0.5, determine
P(A and B).
-----
P(A and B) = P(A) + P(B) - P(A or B)
---
= 0.7 + 0.5 - 0.3
----
= 0.9
================
Cheers,
Stan H.
============
( 0.90
0.45
0.27
0.15
|
Money_Word_Problems/568363: John sold you a candy bar for $1.00 that he bought for only 25 cents. What was the percent of increase?
1 solutions
Answer 366929 by stanbon(57290) on 2012-02-06 08:25:30 (Show Source):
You can put this solution on YOUR website!John sold you a candy bar for $1.00 that he bought for only 25 cents. What was the percent of increase?
Quantity increase 0.75
Percent increase : 0.75/0.25 = 300%
======================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/568352: p: The house is owned by an engineer
q: The heat is solar generated
r: The car is run by electric power
Translate the statement into symbols, then construct a truth table and determine under what conditions the compound statement is true.
The house is owned by an engineer and the heat is solar generated, or the car is run by electric power.
I've gotten the first two columns down for the table
p q
1 t t
2 t t
3 t f
4 t f
5 f t
6 f t
7 f f
8 f f
Not sure how to continue or to label.
1 solutions
Answer 366924 by stanbon(57290) on 2012-02-06 08:03:46 (Show Source):
You can put this solution on YOUR website!p: The house is owned by an engineer
q: The heat is solar generated
r: The car is run by electric power
Translate the statement into symbols, then construct a truth table and determine under what conditions the compound statement is true.
The house is owned by an engineer and the heat is solar generated, or the car is run by electric power.
-----
p AND q OR r
---------------------
I've gotten the first two columns down for the table
..p q r
1 t t t
2 t t f
3 t f t
4 t f f
5 f t t
6 f t f
7 f f t
8 f f f
====================
Cheers,
Stan H.
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Permutations/568356: how many bridge hands are possible containing 4 spades,6 diamonds,1 club, and 2 hearts?
1 solutions
Answer 366923 by stanbon(57290) on 2012-02-06 07:58:40 (Show Source):
You can put this solution on YOUR website!how many bridge hands are possible containing 4 spades,6 diamonds,1 club, and 2 hearts?----
---------------------------
Ans: 13C4*13C6*13C1*13C2 = 1244117160
=============
Cheers,
Stan H.
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Polygons/568358:
A polygon has n sides.There of its exterior angles are 70 degree, 25 degree, 15 degree while the remaining (n-3) exterior angles are each equal to 50 degree.Find n.
affiliate network, pandora, limewire
1 solutions
Answer 366922 by stanbon(57290) on 2012-02-06 07:54:51 (Show Source):
You can put this solution on YOUR website!A polygon has n sides.There of its exterior angles are 70 degree, 25 degree, 15 degree while the remaining (n-3) exterior angles are each equal to 50 degree.Find n.
----
Sum of the exterior angles is always 360.
Equatiion:
(n-3)50+70+25+15 = 360
(n-3)50+110 = 360
(n-3)= 250/50 = 5
n = 8
=================
cheers,
Stan H.
=================
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absolute-value/568353: y= (x+4)-(x+1)
the (brackets) are supposed to be the absolute value bar lines
i understand how to get a resulting graph by graphing both vectors and adding the y values from left to right and then plotting the points.
my question is what is the resulting graph supposed to tell you?
i'm confused because i don't really get how to read the graph
i have worked out that the resulting graph looks like a rigid S shape from using an algebraic method
for x<-2
y= -(x+2) +(x+1)
= -x-2+x+1
y=-1
for -2
y=x+2+x+1
y=2x+3
for x>-1
y=x+2-x-1
y=1
if i graph these 3 equations, i will get the same resulting graph.
does it mean the points on the resulting graph are the solutions?
thanks in advance.
1 solutions
Answer 366921 by stanbon(57290) on 2012-02-06 07:51:04 (Show Source):
You can put this solution on YOUR website!y= |x+2|-|x+1|
--------------------
for x<-2
y= -(x+2) +(x+1)
= -x-2+x-1
-----------------------
for -2
y=x+2+x+1
y=2x+3
------------------------
for x >-1
y=x+2-x-1
y=1
---------------------------
if i graph these 3 equations, i will get the same resulting graph.
does it mean the points on the resulting graph are the solutions?
----
Ans: Yes
====================
Cheers,
Stan H.
====================
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Polynomials-and-rational-expressions/568349: Please help me find the x-intercepts and the y-intercepts for F(x)= -x^2 + 2x + 24
Thank you
1 solutions
Answer 366920 by stanbon(57290) on 2012-02-06 07:41:41 (Show Source):
You can put this solution on YOUR website!find the x-intercepts and the y-intercepts for F(x)= -x^2 + 2x + 24
-----
y-intercept = ?
Let x = 0 ; then y = 24
---------------
x-intercept = ?
Let y = 0 and solve for "x":
-x^2+2x+24 = 0
---
x^2-2x-24 =0
(x-6)(x+4) = 0
x = 6 or x = -4
==================
Cheers,
Stan H.
==================
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Polynomials-and-rational-expressions/568336: Problem is F(x) = -(x-2)^2 -7 I need to find the vertex , line of symmetry, maximum/minimum value I am not sure if I am doing these problems right can anyone help me with a step by step? Thanks
1 solutions
Answer 366919 by stanbon(57290) on 2012-02-06 07:26:13 (Show Source):
You can put this solution on YOUR website!The equation is in vertex form.
Notice that is x = 2, y will be -7
Notice that any other value of x will result
in y being a value more negative than -7
----------------------------------------------
F(x) = -(x-2)^2 -7 I need to
find the vertex (2,-7)
-----
line of symmetry:: x = 2
---------
maximum/minimum value::: max = -7
==================
Cheers,
Stan H.
|
Numbers_Word_Problems/568289: Sum of 4 consecutive ODD numbers is 224. Find the numbers__, _ _ _
1 solutions
Answer 366896 by stanbon(57290) on 2012-02-05 23:02:58 (Show Source):
You can put this solution on YOUR website!Sum of 4 consecutive ODD numbers is 224. Find the numbers__, _ _ _
---
1st: 2x-3
2nd: 2x-1
3rd: 2x+1
4th: 2x+3
----
Equation:
sum = 224
8x = 224
x = 28
------
1st: 2x-3 = 53
2nd: 55
3rd: 57
4th: 59
==================
Cheers,
Stan H.
|
Numbers_Word_Problems/568290: The product of 2 consecutive EVEN numbers is 528 find the numbers
1 solutions
Answer 366895 by stanbon(57290) on 2012-02-05 23:00:22 (Show Source):
You can put this solution on YOUR website!The product of 2 consecutive EVEN numbers is 528 find the numbers
---
1st: 2x
2nd: 2x+2
----
Equation:
2x(2x+2) = 528
4x(x+1) = 528
x(x+1) = 132
x^2+x-132 = 0
(x-11)(x+12) = 0
---
If x = 11; 2x = 22 and 2x+2 = 24
----
If x = -12; 2x = -24 and 2x+2 = -22
===========================================
cheers,
Stan H.
================
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Linear-equations/568280: The costs C and income I for making and selling T-shirts with a school logo are given by the equations C=$535+4.50n and I=$12n, where n is the number of T-shirts.
a. How many T-shirts must be bought and sold to break even? Explain. I got that the answer to this one is $72 as you cannot make 71.3 shirts.
b. Suppose only 50 shirts are sold. Is there a profit or loss. I said Loss.
C. Suppose the income is $1,200. Is there a profit or loss. I said profit.
WHERE I NEED HELP
d. i. For each equation, find the coordinates of a point that lies on the graph of the equation.
ii. What information does this point give?
iii. Describe how to use the equation to see that the point will be on the graph.
I can't remember how to put these equations on a graph.
Please help. Thank you
1 solutions
Answer 366894 by stanbon(57290) on 2012-02-05 22:56:45 (Show Source):
You can put this solution on YOUR website!The costs C and income I for making and selling T-shirts with a school logo are given by the equations C=$535+4.50n and I=$12n, where n is the number of T-shirts.
a. How many T-shirts must be bought and sold to break even? Explain. I got that the answer to this one is $72 as you cannot make 71.3 shirts.
C=$535+4.50n and I=$12n
535+4.5n = 12n
535 = 6.5n
n = 72 when rounded up
====================================
b. Suppose only 50 shirts are sold. Is there a profit or loss. I said Loss.
OK
-----------------------
C. Suppose the income is $1,200. Is there a profit or loss. I said profit.
So n would be 100 : So profit.
----------------------------
WHERE I NEED HELP
d. i. For each equation, find the coordinates of a point that lies on the graph of the equation.
ii. What information does this point give?
That is the equilibrium point (72,864).
That is where I = C
------------------------
iii. Describe how to use the equation to see that the point will be on the graph.
Replace n and C with the numbers
Replace n = I with the numbers
Since (72,864) satisfies both equations that
point is the solution for the system of
two equations.
====================
Cheers,
Stan H.
==============
====================================
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Rational-functions/568277: Find the variation constant and an equations and variables where y varies inversely as x and y=9 when x=13
1 solutions
Answer 366892 by stanbon(57290) on 2012-02-05 22:35:12 (Show Source):
You can put this solution on YOUR website!Find the variation constant and an equations and variables where
y varies inversely as x
---
y = k/x
Solve for "k" using "y=9 when x=13".
-----
9 = k/13
k = 13*9
k = 117
===============
Cheers,
Stan H.
==============
|
absolute-value/568278: absolute value l -10-10a l < 60 (the l are the absolute value signs) I know the answer is a<5 and a>-7. I just don't know how to get that answer.
Thank you!
1 solutions
Answer 366889 by stanbon(57290) on 2012-02-05 22:29:42 (Show Source):
You can put this solution on YOUR website!| -10-10a | < 60
----
-60 < -10-10a < 60
Add 10 along the line:
-50 < -10a < 70
---
Divide thru by -10.
Remember to reverse the inequality when you divide by a negative:
-7 < a < 5
=============================
Cheers,
Stan H.
|
Money_Word_Problems/568281: If a business borrows $15,000 and repays $21,300 in 4 years, what is the simple interest rate?
1 solutions
Answer 366887 by stanbon(57290) on 2012-02-05 22:24:02 (Show Source):
You can put this solution on YOUR website! If a business borrows $15,000 and repays $21,300 in 4 years, what is the simple interest rate?
--------
A(t) = P(1+rt)
21300 = 15000(1 + r*4)
1.42 = 1 + 4r
4r = 0.42
r = 0.1050 = 10.5%
======================
Cheers,
Stan H.
================
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Probability-and-statistics/568103: a study was conducted in oder to determine if any link existed between cellular phone usage and the development of brain cancer. Data from this study indicate that normally phone usage for all users is approximately normally distributed with mean 2.4 hours and standard deviation 1.1 hours.
a. what proportion of cell phone users are on their phones between 1 hour an 3 hours per month?
b. just to be safe, suppose you decide to be in the 5th percentile of cell phone users in terms of monthly usage. how much time can you spend on the phone this month?
1 solutions
Answer 366846 by stanbon(57290) on 2012-02-05 16:43:11 (Show Source):
You can put this solution on YOUR website!a study was conducted in order to determine if any link existed between cellular phone usage and the development of brain cancer. Data from this study indicate that normally phone usage for all users is approximately normally distributed with mean 2.4 hours and standard deviation 1.1 hours.
a. what proportion of cell phone users are on their phones between 1 hour an 3 hours per month?
z(1) = (1-2.4)/1.1 = -1.2727
z(3) = (3-2.4)/1.1 = 0.5455
---
P(1 <= x <= 3) = P(-1.2727<= z <= 0.5455) = 0.6057
--------------------------------------------------------------
b. just to be safe, suppose you decide to be in the 5th percentile of cell phone users in terms of monthly usage. how much time can you spend on the phone this month?
Ans:invNorm(0.05) = -1.645
----
x = zs + u
x = -1.645*1.1 + 2.4 = 0.5905 hours = 35.43 minutes
===================
Cheers,
Stan H.
===================
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