You roll two dice. What is the probability that the average of the high and low roll is exactly 3, to four decimal places?
1 answer:
Answer:
0.1111
Step-by-step explanation:
Given that you roll two dice.
the average of the high and low roll is exactly 3,
Since die can show only 1 to 6 we can say average can be 3 in each of the following case.
(1,5) (2,4) (3,3) (4,2) (5,1)
There cannot be any other combination to get average of 3.
Thus favourable events = 4
Sample space will have
(1,1)...(1,6)
(2,1)....
(6,1)...(6,6) i.e. 36
So probability that the average of the high and low roll is exactly 3
=
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Answer:
The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48 cubic units.
Step-by-step explanation:
Rotation about x-axis or y-axis at an angle requires some general rules. When a 2D figure is rotated about a line a 3d figure would be produced. This can be done through a process called solid of revolution.
From the question, connecting the given coordinates produces a rectangle with a length of 4 units and width 3units.
Area of the rectangle = Length × width
= 4 × 3
= 12 square units
The required rule for rotation of a figure about y-axis is: (x, y) → (-y, x).
If the given rectangle is rotated about y-axis, a cylinder would be formed.
The volume of the cylinder = V = h
where: r = 4 units and h = 3 units.
V = ×
× 3
= 48 cubic units
Therefore, the rotation of the rectangle of area 12 squared units produces a cylinder with volume of 48 cubic units.
Answer:
No. Once the confidence interval is calculated, the probability that it contains the true mean is either 1 or 0. So then is not appropiate says that the confidence level is a chance. The best conclusion for this case would be:
We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)
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".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
After apply the procedure we got that the interval is (0.02; 0.045) and we need to analyze if the following conclusion is right or no:
She says that there is a 99% chance that the true mean is between 0.020 and 0.045. Is she right? Why or why not?
The best answer for this case would be:
No. Once the confidence interval is calculated, the probability that it contains the true mean is either 1 or 0. So then is not appropiate says that the confidence level is a chance. The best conclusion for this case would be:
We have 99% confidence that the true mean for the variable of interest on this case is between (0.02; 0.045)