Ralph bought 3 boxes with 20 pencils each and 4 boxes with 10 pens each. To find the total number of pencils and pens, Ralph eva
2 answers:
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Answer:
The 99% confidence interval would be given by (0.697;0.903)
And the best option is : 0.697 to 0.903
Step-by-step explanation:
Previous concepts
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".
Solution to the problem
For this case the conditions we have the conditions to assume a normal distribution for the population proportion since:
np=100*0.8=80 >10 , n(1-p) = 10*(1-0.8) =20 >10
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
The estimated proportion is given by . If we replace the values obtained we got:
The 99% confidence interval would be given by (0.697;0.903)
And the best option is : 0.697 to 0.903
Answer: 48 degrees
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See the attached image for a visual of the problem and answer.
Based on the diagram, we have angle AHB = 132 degrees (given) equal in measure to angle XHY since these two angles are vertical angles.
Angles HYC and HXC are right angles due to the nature of AX and BY being altitudes. Recall that altitudes are segments that go from one vertex to the opposite side and they are perpendicular to the opposite side.
Focus on quadrilateral HXCY. So far, we know that...
Angle XHY = 132 degrees
Angle HYC = 90 degrees
Angle HXC = 90 degrees
The angle we want to find is angle ACB, which is the same as angle YCX. This angle is the missing angle of the quadrilateral HXCY.
For any quadrilateral, the four angles must add to 360 degrees.
(angle XHY) + (angle HYC) + (angle HXC) + (angle YCX) = 360
(132) + (90) + (90) + (angle YCX) = 360
312 + (angle YCX) = 360
312 + (angle YCX) - 312 = 360 - 312
angle YCX = 48 degrees
Since angle ACB is the same as angle YCX, we can say
angle ACB = angle YCX = 48 degrees
So in summary,
angle ACB = 48 degrees
-------------------------------------------------------
See the attached image for a visual of the problem and answer.
Based on the diagram, we have angle AHB = 132 degrees (given) equal in measure to angle XHY since these two angles are vertical angles.
Angles HYC and HXC are right angles due to the nature of AX and BY being altitudes. Recall that altitudes are segments that go from one vertex to the opposite side and they are perpendicular to the opposite side.
Focus on quadrilateral HXCY. So far, we know that...
Angle XHY = 132 degrees
Angle HYC = 90 degrees
Angle HXC = 90 degrees
The angle we want to find is angle ACB, which is the same as angle YCX. This angle is the missing angle of the quadrilateral HXCY.
For any quadrilateral, the four angles must add to 360 degrees.
(angle XHY) + (angle HYC) + (angle HXC) + (angle YCX) = 360
(132) + (90) + (90) + (angle YCX) = 360
312 + (angle YCX) = 360
312 + (angle YCX) - 312 = 360 - 312
angle YCX = 48 degrees
Since angle ACB is the same as angle YCX, we can say
angle ACB = angle YCX = 48 degrees
So in summary,
angle ACB = 48 degrees