Consider the expression: (x + 3)•(y + 1)•(x + 2)
1 answer:
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Answer:
a) The 99% confidence interval would be given (0.204;0.296).
b) We have 99% of confidence that the true population proportion of all seafood sold in the country that is mislabeled or misidentified is between (0.204;0.296).
c) No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.
Step-by-step explanation:
Part a
Data given and notation
n=580 represent the random sample taken
X represent the seafood sold in the country that is mislabeled or misidentified by the people
estimated proportion of seafood sold in the country that is mislabeled or misidentified by the people
represent the significance level (no given, but is assumed)
p= population proportion of seafood sold in the country that is mislabeled or misidentified by the people
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
The confidence interval would be given by this formula
For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 99% confidence interval would be given (0.204;0.296).
Part b
We have 99% of confidence that the true population proportion of all seafood sold in the country that is mislabeled or misidentified is between (0.204;0.296).
Part c
A government spokesperson claimed that the sample size was too small, relative to the billions of pieces of seafood sold each year, to generalize. Is this criticism valid?
No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.
The picture in the attached figure
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²