Q: Find the standard deviation when the mean is 100 and 2.68 of the area lies to the right of 105?

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One standard deviation

The area between the mean and 1 standard deviation above or below the mean is about 0.3413 or 34.13%

The answer will depend on the distribution of the variable.

Convert to Standard Normal Distribution the values of 1.22 & 8.78. Z = (8.78-5)/1.41 = 2.68; and Z = (1.22-5)/1.41 = -2.68. Find the area between 2.68 & -2.68 from Table. Area @ 2.68 = .9963; Area @ -2.68 = .0037. Take the difference in the areas and that is the solution. 0.9963 - 0.0037 = .9926 or 99.26% of the scores fall between 1.22 & 8.78.

Each standard deviation represents a certain percentile. So if we use two decimal places, −3 is the 0.13th percentile, −2 the 2.28th percentile, −1 the 15.87th percentile, 0 the 50th percentile , +1 the 84.13th percentile, +2 the 97.72th percentile, and +3 the 99.87th percentile.The mean, median and mode are all the same it the distribution is normal.BUT WHY DOES THIS WORK? HOW DO YOU DO IT?The main idea to make all this work and understandable is that the area under the normal curve is one. So if you have a SD and a mean, you can find the z score.Then, using a calculator, or a table, or even sometimes just some rules you may have learned like the empirical rule, you can find the area to the left or right of any given z score. This area is actually a percentile!So for example, if convert a data point to a z - score using the mean and standard deviation ( The formula is z=(x-mean)/standard deviation, by the way), and I look up the probability of that z-score, and say it is .25. Then it is the 25th percentile.The table below gives you all the percentiles and their corresponding z scores.z-score percentile for normal distributionPercentilez-ScorePercentilez-ScorePercentilez-Score1-2.32634-0.412670.442-2.05435-0.385680.4683-1.88136-0.358690.4964-1.75137-0.332700.5245-1.64538-0.305710.5536-1.55539-0.279720.5837-1.47640-0.253730.6138-1.40541-0.228740.6439-1.34142-0.202750.67410-1.28243-0.176760.70611-1.22744-0.151770.73912-1.17545-0.126780.77213-1.12646-0.1790.80614-1.0847-0.075800.84215-1.03648-0.05810.87816-0.99449-0.025820.91517-0.954500830.95418-0.915510.025840.99419-0.878520.05851.03620-0.842530.075861.0821-0.806540.1871.12622-0.772550.126881.17523-0.739560.151891.22724-0.706570.176901.28225-0.674580.202911.34126-0.643590.228921.40527-0.613600.253931.47628-0.583610.279941.55529-0.553620.305951.64530-0.524630.332961.75131-0.496640.358971.88132-0.468650.385982.05433-0.44660.412992.326

Related questions

You cannot calculate standard deviation for objects such as concrete cubes - you can only calculate standard deviation for some measure - such as side length, surface area, volume, mass, alkalinity or some other measure.

One standard deviation

The area under N(0,1) from -1 to 1 = 0.6826

The area between the mean and 1 standard deviation above or below the mean is about 0.3413 or 34.13%

The answer will depend on what the variable is: turnover, profit, floor area, number of customers, etc.

The area within the normal curve between -1 standard deviation (SD) and +1 SD is approximately 68%. This means that about 68% of the data falls within one standard deviation of the mean in a normal distribution.

The answer will depend on the distribution of the variable.

The empirical rule is 68 - 95 - 99.7. 68% is the area for +/- 1 standard deviation (SD) from the mean, 95% is the area for +/- 2 SD from the mean; and 99.7% is the area for +/- 3 SD from the mean.

From the table in the related link, the value at z equal one is 0.3413. The area then to the right of z equal one is 0.5 - 0.3413, or 0.1587.

how to find the perimeter of a right angled triangle using the area

Convert to Standard Normal Distribution the values of 1.22 & 8.78. Z = (8.78-5)/1.41 = 2.68; and Z = (1.22-5)/1.41 = -2.68. Find the area between 2.68 & -2.68 from Table. Area @ 2.68 = .9963; Area @ -2.68 = .0037. Take the difference in the areas and that is the solution. 0.9963 - 0.0037 = .9926 or 99.26% of the scores fall between 1.22 & 8.78.

Assuming a normal distribution: For the fastest 5% we need to find the z value which gives 100% - 5% = 95% of the area under the normal curve (from -∞). Using single tailed tables, we need the z value which gives 95% - 50% = 0.45 (above the mean); this is found to be z ≈ 1.645 z = (value - mean)/standard deviation → value = mean + z × standard deviation ≈ 5 min 17 sec + 1.645 × 12 sec ≈ 5 min 17 sec + 20 s = 5 min 37 sec