Answer:
99.7%
Step-by-step explanation:
Given that mean (μ) = 394.3 ms and standard deviation (σ) = 84.6 ms.
The empirical rule states that for a normal distribution:
- 68% falls within one standard deviation (μ ± σ)
- 95% falls within two standard deviation (μ ± 2σ)
- 99.7% falls within three standard deviation (μ ± 3σ)
one standard deviation = 394.3 ± 84.6 = (309.7, 478.9). 68% falls within 309.7 and 478.9 ms
two standard deviation = 394.3 ± 2 × 84.6 = (225.1, 563.5). 95% falls within 225.1 and 563.5 ms
three standard deviation = 394.3 ± 3 × 84.6 = (140.5, 648.1). 99.7% falls within 140.5 and 648.1 ms
Answer:
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Step-by-step explanation:
Let n = required random sample size.
Assume that the population standard deviation is known as σ.
Let m = sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.
Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²
This means that the sample size is about 128 times the population variance.
Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.
Answer:
Step-by-step explanation:
First we'll work out the surface area of the pink figure.
That's the area of the two 5 by 6 rectangles on the top and bottom, plus the area of the two 5 by 20 and two 6 by 20 rectangles on the sides.
However, we note that the purple figure is blocking out a 6 by 12 section on the pink figure, so we'll need to subtract this.
The above works out to 
.
Then we'll work out the surface area of the purple figure.
This will be the area of the two 4 by 6 rectangles at the top and bottom, plus the area of the two 4 by 12 and one 6 by 12 rectangles on the sides. Note that there's only one 6 by 12 rectangle because the other face is joined to the pink figure, so it's blocked out.
That's 
.
So the total surface area is 
.
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