A soda manufacturer claims that on average their bottles contain 16oz of soda with an SD of 0.1oz. A regulatory agency decides t
o test this claim by randomly sampling 100 bottles. They actually observe a sample average of 15.5 oz. What are the chances that they would get a sample average of 15.5oz or less in a sample of this size
1 answer:
Answer: The chances are of the probability = 0.0001
Step-by-step explanation:
The normal distribution can be described completely by the two parameters µ and σ.
As always, the mean is the center of the distribution and the standard deviation is the measure of the variation around the mean.
Please find the attached file for the solution
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Answer:
d = 2cot(x) or d = 2/tan(x)
Step-by-step explanation:
The vertical distance from the jet to the top of the house represents the opposite side to the 'x' angle, while the horizontal distance, d, represents the adjacent side. Since we do not know the hypotenuse, the tangent and cotangent functions are the preferable choices:
Therefore, the distance 'd' can be expressed as d = 2cot(x) or d = 2/tan(x).
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
