Mathematics, 12.02.2020 01:43 miagiancarlo

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is Select one: a. less than 2 b. 2 c. greater than 2 d. 3

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Answer from: kelyanthecrafte

The standard error of the mean is 2.

given,

Number of sample is 49.

The standard deviation of sample is 14.

We know that, the standard error of the mean is calculated by dividing the standard deviation by the square root of sample selected.

$\rm SE=\dfrac{\sigma}{\sqrt{n} }$

Here $\sigma$ is the standard deviation and n is the number of sample.

So,

$\rm SE=\dfrac{14}{\sqrt{49} }$

$\rm SE=\dfrac{14}{7}$

$\rm SE =2$ .

Hence the correct option will be (b). 2

For more details on Standard error of the mean follow the link:

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Answer from: Yoma321

b. 2

Step-by-step explanation:

The Central Limit Theorem is important to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ . This standard deviation, of the sample, is also called standard error of the mean.

In this problem, we have that:

$\sigma = 14, n = 49$

The standard error of the mean is

$\frac{14}{\sqrt{49}} = 2$

So the correct answer is:

b. 2

Answer from: Quest

geometric series converge the common ratio r has magnitude less than one.

$|r| < 1$

which is equivalent to

$-1 < r < 1$

for the example we need

|2-x| < 1

-1 < 2-x and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1 diverges

1b. r=50/100=1/2 converges

when these converge they converge to

$s = \dfrac{a}{1 -r}$

where a is the first term.

$s = \dfrac{100}{1 - 1/2} = 200$

answer: 200

1c. r=-1 so it's not the case that |r| < 1. diverges

2a. x is the common ratio so we converge when |x|< 1

2b. r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c. r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

$|x| < \frac 1 2 \sqrt[3]{2}$

Answer from: Quest

none of the above.

for one of the equations to be used in the process, there has to be a $2x^2$ term in the equation since $2x$ squared is $2x^2$ .

since there is only a $x^2$ term in the first equation, we cannot derive a $2x+4$ from completing the square.

solving with completing the square

$x^2=-4x+3$

$x^2+4x=3$

$x^2+4x+4=7$

$(x+2)^2=7$

$x+2=+-\sqrt{7}$

$x=2+-\sqrt{7}$

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