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Anna007 [38]
3 years ago
6

g The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9 hour. What assumptions must be true

to use the result of the central limit theorem to obtain a valid approximation for probabilities about the average daily downtime
Mathematics
1 answer:
Sedaia [141]3 years ago
7 0

Answer:

To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.

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Answer:

a) 1/27

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c) 1/8

Step-by-step explanation:

a) x^{-3/2}

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

x^{-3/2}=\frac{1}{x^{3/2} }

And now, solving for x = 9 we have:

\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} }  =\frac{1}{27}

b) y^{4/3}

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

y^{4/3}=8^{4/3}=16

c) z^{-3/4}

Using the same property we used in a) we have:

z^{-3/4}=\frac{1}{z^{3/4} }

And now, solving for z = 16 we have:

\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}

4 0
3 years ago
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alukav5142 [94]

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6 0
3 years ago
49 is 35% of what number?
NNADVOKAT [17]
We write this like this:

49=35%x

and we want to find the x.

let's invert the sides:

35%x=49.


35 is equal to 0.35

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(aternatively we can do it through fractions:

35/100*x=49
divide both sides by 7:

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