Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 195,
1 answer:
Given:
n = 195, sample size.
x = 162, successes in the sample
The proportion is
p = x/n = 162/195 = 0.8308
n* p = 195*0.8308 = 162
n*(1-p) = 195*(1 - 0.8308) = 33
If n*p >= 10, and n*(1-p) >= 10, then the sample proportions will have a normal distribution. This condition is satisfied.
The proportion mean is
μ = 0.8308
The proportion standard deviation is
σ/√n = 0.0269/√195 = 0.00192
At the 95% confidence level, the interval for the population proportion is
(μ - 1.96(σ/√n), μ + 1.96(σ/√n))
= (0.8308 - 1.96*0.00192, 0.8308 + 1.96*0.00192)
= (0.827, 0.8345)
Answer: The 95% confidence interval is (0.827, 0.835)
n = 195, sample size.
x = 162, successes in the sample
The proportion is
p = x/n = 162/195 = 0.8308
n* p = 195*0.8308 = 162
n*(1-p) = 195*(1 - 0.8308) = 33
If n*p >= 10, and n*(1-p) >= 10, then the sample proportions will have a normal distribution. This condition is satisfied.
The proportion mean is
μ = 0.8308
The proportion standard deviation is
σ/√n = 0.0269/√195 = 0.00192
At the 95% confidence level, the interval for the population proportion is
(μ - 1.96(σ/√n), μ + 1.96(σ/√n))
= (0.8308 - 1.96*0.00192, 0.8308 + 1.96*0.00192)
= (0.827, 0.8345)
Answer: The 95% confidence interval is (0.827, 0.835)
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Let the length of a side of a cube = x unit
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Where r = radius of the sphere = units
36π =
36π =
36×24 = 4x³
x =
x = 6 units
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= 6×(6)²
= 216
= 216 square units
Answer:
a)
b)
c)
When the acceleration is 0 we have:
And if we replace t=2 in the velocity function we got:
Step-by-step explanation:
For this case we have defined the following function for the position of the particle:
Part a
From definition we know that the velocity is the first derivate of the position respect to time and the accelerations is the second derivate of the position respect the time so we have this:
Part b
For this case we need to analyze the velocity function and where is increasing. The velocity function is given by:
We can factorize this function as
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For this case if we select two values let's say 0.25 and 0.5 we see that
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We have a minimum at t=2 since at this value w ehave the vertex of the parabola :
And at t=-2 v(2) = -3 that represent the minimum for this function, we see that if we select two values let's say 1.5 and 1.75
v(1.75) =-2.8125< -2.25= v(1.5) so then the function sis decreasing on the interval 1<t<2
We see that the function would be increasing.
For this interval we will see that for any two points a,b with we have
for example let's say a=3 and b =4
The particle is moving to the right then the velocity is positive so then the answer for this case is:
Part c
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And if we replace t=2 in the velocity function we got:
I'm not sure what the question is here. If an answer is communicative property, go with that. If it is asking for , the answer is about 84.8230016469.