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Finite Math Problems
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Finite Math Problems

by Ken Howard
(Houston, TX, USA)








































I need help for some questions below:

Pls, show me steps by steps .

1) I don't know how to write a matrix to display the information in Finite math.

2) Solve the matrix for X .

A=[5 3 ,B=[[-6
8 5
] -2]], AX=B.
3) Write the indicated event in set notation for the experiment described as :
A die is tossed twice with the tosses recorded as an order pair. Represent the following events as a subset of the sample space: the first toss shows a six.

4) A die is tossed twice with the tosses recorded as an order pair.Represent the following events as a subset of the sample space: The sum of the tossed is either three or four.

5) A die is tossed twice with the tosses recorded as an order pair. Represent the following event as a subset of the sample space: both tosses show an event number.

6) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space : The second toss shows a two.

7) How to find the percent of the area under a normal curve between the mean and 2.41 deviations from the mean?

8) How to find the percent of the area under the standard normal curve between Z=0.54 and Z=1.91.

9) How to find a Z-score satisfying the given condition.
4% of the total area is to the right of Z.

10)How to find the standard deviation.
7,15,20,19,18,20,17,11,6

Thank you so much for your assistances!!!
I am very nice to meet your wonderful group .

Best regard,

Ken Howard



Comments for Finite Math Problems

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May 14, 2011
Sets, Subsets, Normal Curve
by: Staff


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Part III



b) Use a calculator with a built in function such as the TI-83 or TI-84

c) Use a z table, such as the table located at:

http://www.intmath.com/counting-probability/z-table.php

look up z = 2.41 standard deviations

area (one side of normal curve) = .4920

double this number = .4920*2 = 98.4%

using the table, the answer to your question is: 98.4%

d) Use a good on-line interactive tool, such as the graphical tool located at:

http://www.stat.berkeley.edu/~stark/Java/Html/NormHiLite.htm

enter lower endpoint of: -2.41
enter upper endpoint of: 2.41

the interactive tool shows the answer to your question is: 98.4%


Note that the results obtained using the interactive tool and the results obtained using the z table agree with one another. The result estimated using 68-95-99.7 rule is only a very rough approximation of the real value.


8) How to find the percent of the area under the standard normal curve between Z=0.54 and Z=1.91.

The answer to question 8 is the same general answer described in question 7: use a calculator with a built in function, a z-table, or an online tool.

Using the on-line interactive tool located at:

http://www.stat.berkeley.edu/~stark/Java/Html/NormHiLite.htm

enter lower endpoint of: 0.54
enter upper endpoint of: 1.91

the interactive tool shows the answer to your question is: 26.7%

9) How to find a Z-score satisfying the given condition.
4% of the total area is to the right of Z.

There are many different answers which will equal 4% of the total area.

To find to the right of any “Z” value, it is probably easiest to use a table:

http://www.intmath.com/counting-probability/z-table.php

Start with beginning “Z” value, and then add 4% (using the values in the table)


10) How to find the standard deviation.

7,15,20,19,18,20,17,11,6


1. Calculate the sample average

average = (6+7+11+15+17+18+19+20+20)/9

average = 14.8

2. Compute each deviation (for each sample) by subtracting the mean from each number in the sample

6 - 14.8 = -8.8

7 - 14.8 = -7.8

11 - 14.8 = -3.8

15 - 14.8 = 0.2

17 - 14.8 = 2.2

18 - 14.8 = 3.2

19 - 14.8 = 4.2

20 - 14.8 = 5.2

20 - 14.8 = 5.2

3. Square each deviation:

(-8.8)^2 = 77.44

(-7.8)^2 = 60.84

(-3.8)^2 = 14.44

(0.2)^2 = 0.04

(2.2)^2 = 4.84

(3.2)^2 = 10.24

(4.2)^2 = 17.64

(5.2)^2 = 27.04

(5.2)^2 = 27.04


4. Add the squares


77.44

60.84

14.44

0.04

4.84

10.24

17.64

27.04

27.04

--------

239.56


5. Divide the total of the squares by the number of original values minus 1

(There are 9 numbers. Therefore, divide each total by 8 since 9 – 1 = 8.)

239.56 ÷ 8 = 29.945

6. Standard Deviation = Square root of result in step 5

Standard Deviation = Sqrt(29.945) = 5.47



Thanks for writing.

Staff
www.solving-math-problems.com



May 14, 2011
Sets, Subsets, Normal Curve
by: Staff


------------------------------------------

Part II

4) A die is tossed twice with the tosses recorded as an order pair.

Represent the following events as a subset of the sample space: The sum of the tossed is either three or four.

S =
{(1,1);(1,2);(1,3);(1,4);(1,5);(1,6);
(2,1);(2,2);(2,3);(2,4);(2,5);(2,6);
(3,1);(3,2);(3,3);(3,4);(3,5);(3,6);
(4,1);(4,2);(4,3);(4,4);(4,5);(4,6);
(5,1);(5,2);(5,3);(5,4);(5,5);(5,6);
(6,1);(6,2);(6,3);(6,4);(6,5);(6,6)}

Since the sum of the two tossed dice is either three or four, the subset of the outcome sample space for the event is:

{(1,2);(1,3);(2,1);(2,2);(3,1)}


5) A die is tossed twice with the tosses recorded as an order pair.

Represent the following event as a subset of the sample space: both tosses show an event number.

The event number is normally the result of the roll.

For example, the event number of the outcome (6,5) is also (6,5). This is also a subset of the sample space.


6) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space : The second toss shows a two.

As before, the sample space is the SET of 36 possibilities:

S =
{(1,1);(1,2);(1,3);(1,4);(1,5);(1,6);
(2,1);(2,2);(2,3);(2,4);(2,5);(2,6);
(3,1);(3,2);(3,3);(3,4);(3,5);(3,6);
(4,1);(4,2);(4,3);(4,4);(4,5);(4,6);
(5,1);(5,2);(5,3);(5,4);(5,5);(5,6);
(6,1);(6,2);(6,3);(6,4);(6,5);(6,6)}

Since the second toss is 2, the subset of the outcome sample space for the event which represents an ordered pair of the first toss, and 2 is:

{(1,2);(2,2);(3,2);(4,2);(5,2);(6,2)}


7) How to find the percent of the area under a normal curve between the mean and 2.41 deviations from the mean?

You cannot calculate this value by hand.

However, there are several ways to find the area under the curve:

a) If you do not have access to a calculator or table, you can estimate the approximate value using 68-95-99.7 rule (called the Empirical Rule):

± 1 standard deviation from the mean = 68% of the normal distribution

± 2 standard deviations from the mean = 95% of the normal distribution

± 3 standard deviations from the mean = 99.7% of the normal distribution

Since your question asks for the area under the normal curve between the mean and 2.41 deviations from the mean, you can estimate the value by interpolation. Since the normal curve is not a linear function, interpolating to get your final result will only be a rough estimate:

Estimate of Area under the curve at ± 2.41 standard deviations

= 95% + (2.41 - 2.00)*(99.7% - 95%)
= 95% + (0.41)*(4.7%)
= 95% + 1.9%
= 96.9%

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May 14, 2011
Sets, Subsets, Normal Curve
by: Staff


Part I

The question:

by Ken Howard
(Houston, TX, USA)

I need help for some questions below:

Pls, show me steps by steps .

1) I don't know how to write a matrix to display the information in Finite math.

2) Solve the matrix for X .

A=[5 3 ,B=[[-68 5 ] -2]], AX=B.


3) Write the indicated event in set notation for the experiment described as :

A die is tossed twice with the tosses recorded as an order pair. Represent the following events as a subset of the sample space: the first toss shows a six.

4) A die is tossed twice with the tosses recorded as an order pair.Represent the following events as a subset of the sample space: The sum of the tossed is either three or four.

5) A die is tossed twice with the tosses recorded as an order pair. Represent the following event as a subset of the sample space: both tosses show an event number.

6) A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space : The second toss shows a two.

7) How to find the percent of the area under a normal curve between the mean and 2.41 deviations from the mean?

8) How to find the percent of the area under the standard normal curve between Z=0.54 and Z=1.91.

9) How to find a Z-score satisfying the given condition.
4% of the total area is to the right of Z.

10)How to find the standard deviation.
7,15,20,19,18,20,17,11,6

Thank you so much for your assistances!!!
I am very nice to meet your wonderful group .

Best regard,

Ken Howard




The answer:

2) Solve the matrix for X .

A=[5 3 ,B=[[-68 5 ] -2]], AX=B.

>>>>>> Scan in this section of your problems (so I can see exactly what you are asking), and then upload the image as a new submission.


3) Write the indicated event in set notation for the experiment described as:

A die is tossed twice with the tosses recorded as an order pair.

Represent the following events as a subset of the sample space: the first toss shows a six.

The sample space for throwing one dice twice is the set of all possibilities.

Since the die has 6 sides, the sample space of two tosses is = 6² = 36

The sample space is a SET of 36 possibilities:

S =
{(1,1);(1,2);(1,3);(1,4);(1,5);(1,6);
(2,1);(2,2);(2,3);(2,4);(2,5);(2,6);
(3,1);(3,2);(3,3);(3,4);(3,5);(3,6);
(4,1);(4,2);(4,3);(4,4);(4,5);(4,6);
(5,1);(5,2);(5,3);(5,4);(5,5);(5,6);
(6,1);(6,2);(6,3);(6,4);(6,5);(6,6)}

Since the first number is 6, the subset of the outcome sample space for the event which represents an ordered pair of a 6, and the second toss is:

{(6,1);(6,2);(6,3);(6,4);(6,5);(6,6)}

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May 15, 2011
Finite math questions
by: Ken Howard

Dear Thomas,

How are you today?? I want to thank you vey much for your assistances !!! Appreciate you and your staff. I am so excited after I understand math problems .

I have one more question about how to use the table 2 . Area under the Normal Curve.
The column under A gives the proportion of the area under the entire curve that is between Z=0 and a positive value of Z.

this table 2 is in the back pages of the textbook: Finite math with application ( 9 edition) by Lial ; Hungerford ; Holcomb.

Pls, help me as soon as you can , because I have final test this after noon . I am so sorry that I knew your website so late .

thank you so much !!!

Ken Howard

May 15, 2011
Using the Z-table for a Normal Curve
by: Staff

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Part II

Example III

If you are trying to determine the area under the curve from z = -infinity to z = +1.3.

1. Use the table to look up the area under curve from z = 0 to z = +1.3.

According to the table, this area is: 0.4032 (or 40.32%)

2. The area under curve from z = -infinity to z = 0 is 0.5.

Remember that the normal curve is symmetrical. The area under the entire curve (from –infinity to + infinity) = 1.

The entire area to the right of z = 0 is exactly 0.5.

The entire area to the left of z = 0 is exactly 0.5.

3. Add these two values: (the z-value from –infinity to z = 0) + (the z-value from z = 0 to z = +1.3)

0.5 + 40.32 = 0.9032 = 90.32%



(i) Click the following link to VIEW this solution GRAPHICALLY; or (iiA) highlight and copy the link, then (iiB) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/normal-curve-z-values-02.png




Thanks for writing.

Staff
www.solving-math-problems.com



May 15, 2011
Using the Z-table for a Normal Curve
by: Anonymous


Part I

It sounds like the z-table in your book gives you the area under ½ of the normal curve (positive z values include everything to the right of z=0, the center of the curve).

This is a standard way of presenting tabular data for the z-table. It is similar to the z-table located at:

http://www.intmath.com/counting-probability/z-table.php

If I understand your question correctly, you are asking how to include z values under the other ½ of the normal curve (negative z values include everything to the left of z=0, the center of the curve).

Example I

If you are trying to determine the area under the curve from z = -1.3 to z = +1.3.

1. Use the table to look up the area under curve from z = 0 to z = +1.3.

According to the table, this area is: 0.4032 (or 40.32%)

2. Double that value: 40.32% * 2 = 80.64%.

The normal curve is symmetrical with respect to z = 0 (the axis of symmetry). The area to the left of z = 0 is “exactly” the same as the area to the right of of z = 0.

(i) Click the following link to VIEW this solution GRAPHICALLY; or (iiA) highlight and copy the link, then (iiB) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/normal-curve-z-values.png


Example II

If you are trying to determine the area under the curve from z = -0.3 to z = +1.3.

1. Use the table to look up the area under curve from z = 0 to z = +1.3.

According to the table, this area is: 0.4032 (or 40.32%)

2. Use the table to look up the area under curve from z = 0 to z = +0.3. (the area from z = 0 to z = +0.3 is exactly the same as it would be from z = -0.3 to z = 0)

According to the table, this area is: 0.1179 (or 11.79%)

3. Add these two values:

40.32% + 11.79% = 52.11%

The area under the curve from z = -0.3 to z = +1.3 is 52.11%.


(i) Click the following link to VIEW this solution GRAPHICALLY; or (iiA) highlight and copy the link, then (iiB) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/normal-curve-z-values-01.png

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