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marin [14]
2 years ago
12

According to the Central Limit Theorem, which statements(s) are TRUE. There may be more than 1 correct answer. A. An increase in

sample size from n = 16 to n = 25 will produce a sampling distribution for the sample means that has a smaller standard deviation. B. The larger the sample size, the more the sampling distribution of sample means will resemble a normal distribution C. The mean of the sampling distribution of sample means for samples of size n = 15 will be the same as the mean of the sampling distribution for samples of size n = 100. D. The mean of a sampling distribution of sample means is equal to the population mean divided by the square root of the sample size. E. The larger the sample size, the more the sampling distribution of sample means resembles the shape of the population.
Mathematics
1 answer:
Liono4ka [1.6K]2 years ago
6 0

Answer:

Options A, B and C are correct.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes 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}}

From the Central Limit Theorem, we have that:

The larger the sample size, the closer to the normal distribution the distribution of sample means is.

No matter the sample size, the mean is the same.

The larger the sample size, the smaller the standard deviation.

The smaller the sample size, the larger the standard deviation.

So the correct options are:

A, B, C

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Answer:

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8 0
3 years ago
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Two sides of a triangle measure 8 cm and 15 cm. Whi[:h could be the length of the third side?
lutik1710 [3]

18 cm is correct .

Step-by-step explanation:

The sum of two smaller sides is greater that the largest side.

It is given that the two sides of a triangle measure 8 cm and 15 cm.

Case 1: Let 8 cm and 15 cm. are smaller side. So,

<em>Third side < 8 + 15</em>

<em>Third side < 23</em>

<em>It means 3rd side must be less than 23</em>

<em>Case 2: Let 15 cm is the largest side.</em>

<em>15 < Third side + 8</em>

15 - 8 < Third side

7 < Third side

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8 0
3 years ago
Express 240 as a product of prime factors.
Sholpan [36]

Answer:

240 = 2 x 2 x 2 x 2 x 3 x 5 or 2^4x3x5

Step-by-step explanation:

               240

              /      \

            2      120                     (240 = 2 x 120)

                   /      \

                 2       60                 (120 = 2 x 60)

                        /      \

                      2       30            (60 = 30 x 2)

                             /      \

                           2       15       (30 = 2 x 15)

                                  /      \

                                3        5

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3 years ago
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Using my TI-84Plus calculator, I figured that P(0 dogs will be adopted) is binompdf(9,0.20,0), or 0.134.  Subtracting this from 1.000, we get 0.866 (answer to this problem).
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