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yan [13]
3 years ago
13

a) In a simple random sample of 1000 faculty taken among all universities in a country, the number of papers published by the in

dividual sampled faculty in the past year had a mean of 1.1 and an SD of 1.8. Does the Central Limit Theorem say that the distribution of the number of papers published by the individual sampled faculty in the past year is roughly normal
Mathematics
1 answer:
larisa86 [58]3 years ago
7 0

Answer:

According to the Central Limit theorem, the distribution is roughly normal

Step-by-step explanation:

The Central Limit Theorem states that for sample sizes above 30 and not withstanding population distribution's shape, the sampling distribution of the sample mean becomes more similar t hat of a normal distribution as the sample size increases;

The size of the sample = 1,000 >> 30

As the sample size approaches infinity, we have;

z=\dfrac{\bar{x}-\mu }{\dfrac{S.D.}{\sqrt{n}}}

\overline x = 1.5

S.D. = 1.8

n = 1000

Assume μ = 1, we get;

P(x > 1.1):z=\dfrac{1.1-1 }{\dfrac{1.8}{\sqrt{1000}}} = 1.7568

P(z > 1.7568) = 1 - 0.96080 = 0.0392

Therefore, it is very likely that the mean of the population is not larger than the sample mean

Therefore, yes, the Central Limit Theorem say that the distribution of the number of papers published by the individual sampled faculty in the past year is roughly normal

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Prove that an = 4^n + 2(-1)^nis the solution to
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Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute a_n=4^n+2(-1)^n in the equation a_n=3a_{n-1}+4a_{n-2} the equality is true.

Let's substitute first in the right hand side:

3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})

Now we use the distributive laws. Also, note that (-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n} (this also works when the power is n-2).

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4 0
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A cylindrical piece of iron pipe is shown below. The wall of the pipe is 0.75 inch thick, and the pipe is open at both ends:
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Answer:

(A)398 cubic inches

Step-by-step explanation:

Given a cylindrical piece of iron pipe with the following dimensions:

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Since the wall of the pipe is 0.75 inch thick,

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We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure
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Answer:

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Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be h(t) = -16\cdot t^{2} + 128\cdot t + 320, the first and second derivatives are, respectively:

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Second Derivative

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Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

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t = 4\,s (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

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h(4\,s) = 576\,ft

The highest altitude that the object reaches is 576 feet.

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3 years ago
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