Answer:
The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
As the sample size is large, i.e. <em>n</em> = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:
Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:
![=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090](https://tex.z-dn.net/?f=%3DP%28%7CZ%7C%3E2.61%29%5C%5C%5C%5C%3D1-P%28%7CZ%7C%5Cleq%202.61%29%5C%5C%5C%5C%3D1-P%28-2.61%5Cleq%20Z%5Cleq%202.61%29%5C%5C%5C%5C%3D1-%5BP%28Z%5Cleq%202.61%29-P%28Z%5Cleq%20-2.61%29%5D%5C%5C%5C%5C%3D1-0.9955%2B0.0045%5C%5C%5C%5C%3D0.0090)
Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Answer:
r = 16
Step-by-step explanation:
Cross multiply:
4 x 20 = r x 5
Simplifying
4 x 20 = r x 5
Multiply 4 x 20
80 = r x 5
Reorder the terms for easier multiplication:
80 = 5r
Solve
80 = 5r
Solve for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-5r' to each side of the equation.
80 + -5r = 5r + -5r
Combine like terms: 5r + -5r = 0
80 + -5r = 0
Add '-80' to each side of the equation.
80 + -80 + -5r = 0 + -80
Combine like terms: 80 + -80 = 0
0 + -5r = 0 + -80
-5r = 0 + -80
Combine like terms: 0 + -80 = -80
-5r = -80
Divide each side by '-5'.
r = 16
Simplify
r = 16
Answer:
❘-12 - 54❘
I hope my answer is correct and helpful.
Answer:
The volume of soil in Darren's planter box is 56 feet³
Step-by-step explanation:
The formula of the volume of a rectangular box is V = l × w × h, where l is its length , w is its width and h is its height
∵ Darren's planter box is seven feet long and four feet wide
∴ l = 7 feet
∴ w = 4 feet
<em>The volume of the soil is equal to the volume of the box using the height of the soil, because the soil takes the shape of the box, so they have the same dimensions of the base</em>
∵ Darren fills the planter box with soil to a height of two feet
∴ h = 2 feet
- Substitute the values of l, w and h in the formula of the volume
∵ V = 7 × 4 × 2
∴ V = 56 feet³
The volume of soil in Darren's planter box is 56 feet³
