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2 answers:
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Correct Answer:
Option C. Camera 2
The greatest angle is always opposite to the side measure greater in length. So first we find the greatest side.
The distance between cameras is:
Camera 1 and Camera 2 : 106 feet
Camera 2 and Camera 3 : 133 feet
Camera 1 and Camera 3 : 151 feet
So the largest side of the triangle is the side between camera 1 and camera 3. So the camera opposite to this side will have to cover to greatest angle. The camera opposite to this side is Camera 2. This scenario is also shown in figure below.
Therefore, Camera 2 had to cover the greatest angle.
Option C. Camera 2
The greatest angle is always opposite to the side measure greater in length. So first we find the greatest side.
The distance between cameras is:
Camera 1 and Camera 2 : 106 feet
Camera 2 and Camera 3 : 133 feet
Camera 1 and Camera 3 : 151 feet
So the largest side of the triangle is the side between camera 1 and camera 3. So the camera opposite to this side will have to cover to greatest angle. The camera opposite to this side is Camera 2. This scenario is also shown in figure below.
Therefore, Camera 2 had to cover the greatest angle.
Answer:
a)
b)
c)
Step-by-step explanation:
1) Previous concepts
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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
3) Part b
From the central limit theorem we know that the distribution for the sample mean is given by:
And using a calculator, excel or the normal standard table we have that:
4) Part c
And using a calculator, excel or the normal standard table we have that: