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: B
Step-by-step explanation:
Because m<7 and m<6 share a vertex and doesn’t share any common sides and they are across from each other which means they are vertical and vertical angles are congruent
Answer:
The money they will have to pay is <u>$861</u>.
Step-by-step explanation:
Given:
The swim team has 41 people on their team.
They need new swim gear the swim caps cost $5 and the swim suit cost $16.
Now, to find the money they will have to pay.
Number of people on the swim team = 41.
Cost of swim caps = $5.
Cost of swim suit = $16.
Now, to get the total money they will have to pay:
<u><em>Number of people on the swim team× (cost of swim caps + cost of swim suit)</em></u>
Therefore, the money they will have to pay is $861.
Answer:
C) 20, 4
Step-by-step explanation:
X = 5y
2x + 5y = 60
substitute in 5y for x: 2(5y) + 5y = 60
10y + 5y = 60
15y = 60
y = 4
x = 5y
x = 5(4) = 20
Answer:
1.19
Step-by-step explanation:
You're trying to figure out what x is here.
So you'll want to isolate the x. That means, get it alone.
Since both sides are equivalent, when you subtract 2.45 from the x side, you also subtract it from the other side too.
x = 3.64 - 2.45
x = 1.19
