Percent Increases are not too difficult to find. First, put our percent (5%) into its decimal form so that we can work with it. To turn a percent into a decimal you divide the percent by 100. If you don't have a calculator on you, whenever you are multiplying by 10... 100... 1000... etc. simply move the decimal place over to the left an equal number of times as the number of zeroes in the number. In the case of 100, move the decimal point over 2 times.
Also, if the decimal point isn't shown then write it (or imagine it) right next to the last digit in the number, like so:
5.%
Moving the decimal 2 to the left (dividing by 100) yields this result: 0.05
Keep in mind 5% and 0.05 are equal, but in the case of 0.05 we can work with it, while we can't work with 5%.
Now, we simply multiply our number of miles by 0.05.
Our answer is what the 5% increase is equal to. And since it is an INCREASE we add it to our amount of miles.
12,000 * 0.05 = 600 miles
12,000 + 600 =12,600 miles is our final answer!
You can also take 5% using a different method. Taking 10% of something is the same as moving the decimal of the original total amount (12,000 miles) over by 1.This is due to the fact that you would be multiplying 12,000 by 0.1 (Which is the same as 1/10... which is the same as dividing by 10). So, if we do that we get: 1,200 = 10% of 12,000
Dividing 1,200 by 2 gives us 5% of 12,000. 1,200 / 2 = 600.
Same answer. You can pick the method you like best. (Also, if you move the decimal point over 2 times you are finding 1% of the number... so 1% of 12,000 is... 120. Multiplying that by 5 gets you 5%. So 120 * 5 = 600. You can use these to help you out, but either method works)
This approach often yields much more accurate results than the trapezoidal rule does. Again we divide the area under the curve into n equal parts, but for this rule n must be an even number because we're estimating the areas of regions of width 2Δx.
In a two tailed test the probability of occurrence is the total area under the critical range of values on both the sides of the curve (negative side and positive side)
Thus, the probability values for a two tailed test as compared to a one tailed test is given by the under given relation -
\
Here
Substituting the given value in above equation, we get -