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Simora [160]
2 years ago
13

As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____. a. binomial distribution b.

Poisson distribution c. normal probability distribution d. hypergeometric distribution
Mathematics
1 answer:
kkurt [141]2 years ago
7 0

Answer:

c. normal probability distribution

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:

By the Central Limit Theorem, it is a normal distribution, so option c.

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[(4x + 15) / 5x)] = 1/2
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One way in which to approach this problem would be to treat it as an equation of ratios and to cross multiply:

<span>[(4x + 15) / 5x)] = 1/2  could be written as:

4x + 15        1
----------- =  ---
     5x           2

Then 8x + 30 = 5x

3x = -30,  and so     x = -10 (answer).  Be certain to check this answer through substitution!

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5 0
2 years ago
Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4 by substituting x = 1 and x = 2. 6x + 11 3(x + 7) 2(3x + 16) 3x
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2(3x+16)

Step-by-step explanation:

Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4

4(x + x + 7) − 2x + 8 − 4

When x=1 , the expression becomes 4(1+1+7)-2(1)+8-4=38

When x=2 , the expression becomes 4(2+2+7)-2(1)+8-4=44

Plug in x=1  and check with each expression

6x + 11 =6(1) +11= 16

3(x + 7) = 3(1+7)= 3(8)= 24

2(3x + 16) = 2(3(1)+16)= 38 , we got same answer when x=1, now check with x=2

2(3x + 16) = 2(3(2)+16)= 44

3x + 16= 3+16= 19

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3 years ago
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