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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
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What is conclusion for additional mathematics project work 2009?
The conclusion for an Additional Mathematics Project Work in 2009 would summarize the key findings and results obtained from the project. It would also mention any limitations encountered during the project and propose further areas of research or improvement for future studies. Additionally, the conclusion might reflect on the overall significance of the project in the context of Additional Mathematics.
How do you make normal distribution curve in Excel?
In An Introduction to Excel's Normal Distribution Functions I presented several figures like the one below. This article explains how to create these figures in Excel.
Even if you have no particular reason to chart a normal curve, you might find the techniques interesting. This is because you might need to use similar techniques when you create other charts.
One general technique that I used in this workbook was to set up two worksheets, a Control worksheet and a Data worksheet.
Let's address each of these separately.
First, however, you might wonder how Excel could produce the colors used for this figure. This link explains how to get the free workbook that uses these colors and the free workbook that I explain how to create below.
Set Up the Control WorksheetIn general, you create a normal curve just as you create any other chart in Excel: You set up the data and then chart it.To set up the data, open a new workbook with at least two worksheets. Name one of these Control and the other Data.
In the Control worksheet, first set up the area shown here.
After you enter the labels in column A, assign them as range names in column B. To do so, select the range A2:B8 and choose Insert, Name, Create. Ensure that only Left Column is checked, then choose OK. Do the same for the range A11:B14.
The numbers in the Settings section are values; enter them as shown. Here's a short explanation of each:
Mean. The average value of your data.
StdDev. The Standard Deviation of your data.
NumRows. The number of rows of data to be plotted.
Zmin. The smallest standard deviation to be plotted.
Zmax. The largest standard deviation to be plotted.
PctClear. The percentage of the unshaded area from the left side of the curve, from .0001% to 99.999%.
PctShade. The percentage of the shaded area from the left side of the curve, from .0001% to 99.999%.
The numbers in the Calculations section are returned by formulas:
ShadeLeft =NORMSINV(PctClear)*StdDev+Mean
NORMSINV is the inverse of NORMSDIST function. Given the probability that a variable is within a certain distance of the mean, it finds the z value...the number of standard deviations. To calculate the extent of the shade at its left side, we multiply the NORMSINV result by the amount of the standard deviation, then add the mean.
ShadeRight =NORMSINV(PctShade)*StdDev+Mean
We use the same logic with the PctShade area as for the PctClear area. By doing so, we define the right side of the shaded area.
CurveMin =Zmin*StdDev+Mean
This formula defines the left side of the curve.
CurveMax =Zmax*StdDev+Mean
This formula defines the right side of the curve.
Set Up the Data SheetThis figure shows the top of the Data sheet. Let's take each of these columns in turn:The Sequence value in column A is a counter, from 1 to the number of rows of data. The counter is for convenience only; it's not used in the formulas. In this example, I used 100 rows.
Enter 1 in cell A2, then select the column from cell A2 through the bottom of your spreadsheet. To do so, hold down Ctrl and Shift; and press the Down arrow key. To enter the values, choose Edit, Insert, Series; enter 100 as the stop value in the Series dialog; then choose OK.
Column B returns the Z values from the lowest value to the highest value:
B2: =Zmin
B3: =(Zmax-Zmin)/(NumRows-1)+B2
Column C calculates the chart's X value for each Z value:
C2: =B2*StdDev+Mean
Column D calculates the chart's Y value:
D2: =NORMDIST(C2,Mean,StdDev,FALSE)
Column E calculates the Y values for the area to be shaded:
E2: =IF(C2>ShadeRight,NA(),IF(C2 Copy cell B3 and the formulas in the range C2:E2 down their columns to the last sequence number, in row 101. To complete this step, assign the labels in row 1 of the Data sheet to the data beneath those labels. To do so, first select the range A1:E101. Choose Insert, Name, Create. In the Create Names dialog, make sure only Top Row is checked; then choose OK. To set up the chart of the normal curve, select the range C2:D101. Choose Insert, Chart, or click the Chart Wizard icon. Under Chart Type, choose XY (Scatter). Under Chart Sub-Type, choose "Scatter with data points connected by smooth Lines without markers." Then choose Finish. If you click on the curve, your formula should look something like this: =SERIES(,Data!$C$2:$C$101,Data!$D$2:$D$101,1) You'll find this formula easier work with if you convert its cell references to range names. To do so, edit the formula to: =SERIES(,NormalCurve.xls!X,NormalCurve.xls!Y,1) Here, NormalCurve.xls is the name of my workbook. Your SERIES formula could have a different name. At this point, your chart should look something like the one shown here. To set up the data series for the shaded area beneath the curve, it's easiest to copy the first data series and then modify it. To copy the data series, first select the curve in the chart. Then select the SERIES formula in the formula bar. Copy this formula by pressing Ctrl+C. Then press Esc to de-select the formula. To paste the data series, first click anywhere on the edge of the chart object. After you do so, the SERIES formula will disappear and the words "Chart Area" will appear at the far left side of your formula bar. To paste the formula, click in the formula bar area and then press Ctrl+V. After you paste the SERIES formula, your chart will look something like this. At this point, the chart displays two identical data series, Series 1 and Series 2. Because we want the curve to be shown on top of the shaded area, we'll modify Series 1 to display the shading, and we'll leave Series 2 undisturbed. To select Series 1, first click on the curve. Then look in your formula bar to see which series you've selected. If you see Series 2, press your Down Arrow key once to select Series 1. With Series 1 displayed in your formula bar, change the formula so that it looks like one of these two versions: =SERIES(,Data!$C$2:$C$101,Data!$E$2:$E$101,1) =SERIES(,NormalCurve.xls!X,NormalCurve.xls!Area,1) You'll use the second version if you have assigned range names as I suggested above. At this point, your chart will look the same as it did before. It's now time to change that condition. With Series 1 selected, choose Format, Selected Data Series. In the Y Error Bars tab, choose to display the Minus version of the error bar, and set the Error Amount to a Percentage value of 100%. Then press OK. Here's your initial result. It doesn't look very good, but at least we're heading in the right direction. We next need to change the format the error bars in two ways. We need to make them thicker, which will eliminate the banding in the shaded area, and we typically will change the color of the shaded area. To format the error bars, first click on the error-bar area in your chart. Choose Format, Selected Error Bars. In the Patterns tab, modify the Line settings. Set its color to any color you prefer. And set the line's weight to its thickest setting. Then choose OK. After you make these changes, your chart should look something like this. Now all you need to do is to clean up the chart slightly. To eliminate the legend at the right, select the Legend object within the Chart Area, and then press Delete. To remove the shading in the Plot Area, first select the Plot Area. Choose Format, Selected Plot Area and set the Area shading to None. Then choose OK. Your chart now will look like this. If you want to format the chart so that it looks more like the figure at the beginning of this article, you need to take several additional steps. First, you assign a color patter to the Chart Area, and remove its border. To do so, select the Chart Area. Choose Format, Selected Chart Area, in the Patterns tab choose a color for the Area and choose None for both the Border. If you want to remove the gridlines, select the chart. Choose Chart, Chart Options. In the Gridlines tab, deselect all axes. Then choose OK. If you want to remove the border, select the Plot Area. Choose Border, Selected Plot Area. Set the Border pattern to None, then choose OK. Finally, to assign a number format to the Y axis, first select the axis. Then choose Format, Selected Axis. In the Number tab choose the Custom category and type in this number format: #,###.00. Then choose OK. Your chart should look something like the one shown here. Now, you merely need to adjust its size as needed. As I mentioned at the beginning of this article, use this link to download a free copy of the workbook described here.
"Pro" is a prefix that typically means "in favor of" or "contributing to." It is often used to indicate support, approval, or intensity.
The disappearance of Neandertals was probably caused by?
a combination of factors, including competition with modern humans, interbreeding, and environmental changes such as climate fluctuations. These factors likely contributed to the decline and eventual extinction of the Neandertals.
Answer is Quota sampling.
Its one of the method of non-probability sampling.
The doctor in Macbeth suggests that the person with unnatural troubles should seek help from the divine (B) for a cure, rather than from sources such as witches, Hecate, or Banquo's ghost. This reflects the belief in the play that supernatural problems should be addressed through holy or divine intervention.
Why are some people consistently unlucky?
Luck can be influenced by various factors such as random chance, perception, and attitude. Some people might perceive themselves as consistently unlucky due to a negative mindset or focusing on negative experiences. It's important to remember that luck is often a combination of randomness and our interpretation of events.
What statistical tests can I use on data collected from quota samples?
The simple answer is you cannot use statistical tests on data collected from quota samples.
Unless the sample was collected using a random sampling technique you cannot have any confidence in the results being representative of the population you are sampling. Quota samples are non random.
However this does not stop researchers from using statistical tests on quota samples, even if the results can be taken with a pinch of salt!
How many permutations of letters in word swimming?
The number of permutations of the letters SWIMMING is 8 factorial or 40,320. The number of distinct permutations, however, due to the duplication of the letters I and M is a factor of 4 less than that, or 10,080.
CRM stand for composite risk management. The CRM probability indicates whether or not a business transaction will actually take place.
Why surveys and polls are good examples of finding probabilities?
because they can help you find your right answer
The question asks for the probability of an even card OR a red card. The term "OR" is key since this is not the same as the probability of drawing an even card and a red card, that is to say an even red card. GIven any two events, A and B P(A or B)=P(A)+P(B)-P(A and B) IF A and B are mutually exclusive, then P(A and B)=0 and this equation becomes P(A)+P(B) However, they are NOT in this case. So let A be the probability the card is even and B the probability it is red. P(A)=20/52 since J, K and Q are neither even nor odd (20=(52-12)/2)) P(B)=26/52 since half the cards are red. P(A and B) is the probability that a card is red AND even. We have 20 even cards, half of them are red and half are black so the odds are 10/52 of being red and even. P (A or B)=20/52+26/52-10/52=9/13
How many ways can you arrange 36 ducks in rows?
You can have:
1 row of 36
2 rows of 18
3 rows of 12
4 rows of 9
or 6 rows of 6, so in total there are 5 ways.
Why t-distributions tend to be flatter and more spread out than normal distribution?
The shape of a t distribution changes with degrees of freedom (df). As the the df gets very large the shape of the t distribution will begin to look similar to that of a normal distribution. However, the t distribution has more variability than a normal distribution; especially when the df are small. When this is the case the t distribution will be flatter and more spread out than the normal distributions.
It is 0.35.
Where can one purchase a rolling tote bag?
There are a number of retailers from where a rolling tote bag can be purchased. These retailers include The Find, Smart Crafts, Amazon and Marks and Spencer.
The probability is
(5 times the number of 6s on the spinner/6 timesthe total number of different positions on the spinner)
A die is rolled what is the probability that the die will show 4 5 or 6?
Assuming a standard die of 6 equivalent sides, the probability is 1 in 2 or 50%.
What is the approximate probability that a human offspring will be female?
P(female offspring) = 0.5 = 1/2
Reason,
In the human genetic system, a male has 'XY' chromosomes
A female has 'XX' chromsomes. I will designate the femle chromosomes as X' & X" to distinguish .
Hence Male is XY
Female is X'X"
They can match in the following manner.
XX' = female
XX" = female
YX' = male
YX" male.
So you can see that there are two female outcomes and two male outcomes, out of a total of four(4) possible outcomes.
So 2/4 = 1/2 = 0.5 in both cases.
Hence P( female outcome) = 0.5
NB In reality, with a deeper understaning of statisitical and genetic analysis, slightly more females are born that males. Also males are slightly weaker at birth, there by making males less likely to survive at birth. This difference is only about M:F :: 49% : 51% , so equality of numbers remains roughly equal.
There are many different selections that could be made. You can figure it out by starting with 50 and then multiplying by each number lower to get all of the possibilities.
What is the probability of drawing a black 7 from a standard 52-card deck?
Probability of drawing a black 7 from a standard 52-card deck is 2/52 or 1/26.
To find the probability that exactly 9 patients are successful, we can use the binomial probability formula. The formula is P(x=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success. Plugging in the values, we have P(x=9) = (12 choose 9) * 0.7^9 * (1-0.7)^(12-9). Calculate this expression to find the probability that exactly 9 patients are successful.
