The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per mile and standard deviation 0.15 grams per mile .
(a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile ?
Never mind, got it. If anyone wants to know how to get it though...
1.5/(sq root of .9)=.01
Solve the equation, then square each side.
Answer=225
Long form:
start with:
0.15 / (square root of n) = 0.01
multiply both sides by (square root of n) which gives you:
0.15 = (0.01) x (square root of n)
divide both sides by 0.01 which gives you:
0.15 / 0.01 = square root of n
both sides to the power of 2:
(0.15 / 0.01)^2 = (square root of n)^2
0.0225 / 0.0001= n
n = 225
Short form:
n = (0.15)^2 / (0.01)^2
n = 0.0225 / 0.0001
n = 225
And by .9 I definitely meant n.....haha
That is a brutal solution lol
Solve what equation? You didn't post an associated equation. and 1.5/sqrt of 0.9 does not equal .01
Then square what? Elaborate please.
To determine the required sample size, we need to use the formula for the standard deviation of the sampling distribution:
Standard Deviation of Sampling Distribution = Standard Deviation of Population / √(Sample Size)
In this case, we want the standard deviation of the sampling distribution to be 0.01 grams per mile.
Given:
Standard Deviation of Population = 0.15 grams per mile
Standard Deviation of Sampling Distribution = 0.01 grams per mile
Let's denote the sample size as n.
Plugging the given values into the formula:
0.01 = 0.15 / √(n)
To solve for n, we need to isolate the variable. Multiply both sides of the equation by √(n):
0.01 * √(n) = 0.15
Now, divide both sides by 0.01:
√(n) = 0.15 / 0.01
Simplify the right side:
√(n) = 15
To solve for n, square both sides:
n = 15²
n = 225
Therefore, a sample size of 225 is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile.