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devlian [24]
2 years ago
5

Suppose a simple random sample of size n is drawn from a large population with mean and standard deviation. The sampling distrib

ution of has mean ​______ and standard deviation ​______.
Mathematics
1 answer:
lubasha [3.4K]2 years ago
3 0

The sampling distribution of x has a mean μₓ = <u> μ </u> and standard deviation σₓ =​ <u> σ/√n </u>.

In the question, we are given that a random sample of size n is drawn from a large population with mean μ and standard deviation σ.

We are asked to find the mean and the standard deviation for the sampling distribution of the variable x for this sample.

The sample mean is regularly distributed, with a mean μₓ = μ and standard deviation σₓ = σ/√n, where n is the sample size, for samples of any size taken from populations that have a normal distribution.

Thus, the sampling distribution of x has a mean μₓ= <u> μ </u> and standard deviation σₓ=​ <u> σ/√n </u>.

Learn more about sampling distribution at

brainly.com/question/14467769

#SPJ4

The provided question is incomplete. The complete question is:

"Fill in the blanks to correctly complete the sentence below.

Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ.

The sampling distribution of x has mean μₓ =​______ and standard deviation σₓ =​______."

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What is true about the graphs of y = x^2 – 2 and y = x^2 + 2?
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Graphs behave differently at various x-inter cepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Suppose, for example, we graph the function. f(x) = (x+3)(x - 2)²(x+1)³.

Notice in the figure below that the behavior of the function at each of the x-intercepts is different.

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3/10 x 5 in a fraction
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How to solve these 3 problems
Bingel [31]

Answer:

  1. a. decay; b. growth; c. decay; d. neither
  2. r = 4; a = 1; y = 1·4^x
  3. a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

  1. exponential functions of the form f(x) = a·b^x
  2. exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

__

<h3>1.</h3>

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

  a. 0.4 < 1 . . . decay

  b. 1.3 > 1 . . . growth

  c. 1/2 < 1 . . . decay

  d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

__

<h3>2.</h3>

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

  an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

  an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

  r = 4; a = 1; f(x) = 1·4^x

__

<h3>3.</h3>

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

 a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

  an = 3(5^n)(5^-1) = (3/5)(5^n)

  b. functional form: f(x) = (3/5)(5^x)

  c. function family: exponential growth functions

 d. y-intercept: (3/5) . . . . read this from the f(x) form

     1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

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