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Vaselesa [24]
3 years ago
13

Assume that population mean is to be estimated from the sample described. Use the sample results to approximate the margin of er

ror and​ 95% confidence interval. Sample​ size, n=64​; sample​ mean, x =69.0 ​cm; sample standard​ deviation, s=4.0 cm
Mathematics
1 answer:
Vikentia [17]3 years ago
3 0

Answer:

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X =69 represent the sample mean for the sample  

\mu population mean

s=4.0 represent the sample standard deviation

n=64 represent the sample size  

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The sample mean \bar X have the following distribution:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

The margin of error for the sample mean is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Since we have the sample standard deviation we can estimate the margin of error like this:

ME=t_{\alpha/2}\frac{s}{\sqrt{n}}

The next step would be find the value of \z_{\alpha/2}, \alpha=1-0.95=0.05 and \alpha/2=0.025

We can find the degrees of freedom like this:

df=n-1=64-1=63

And we can find the critical value with the following code in excel for example: "=T.INV(0.025,63)" and we got:

t_{\alpha/2}=\pm 1.998

And the margin of error would be :

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

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2 years ago
The perimeter of a rectangular field is 372 yards. If the width of the field is 87 yards, what is its length?__yards
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ANSWER

The length of the rectangular field is 99 yards

EXPLANATION

Given information

The perimeter of a rectangle field is 372 yards

The width of the field is 87 yards

To find the length of the rectangular field, follow the steps below

Step 1: Write the formula for finding the perimeter of a rectangular field

\begin{gathered} \text{ The perimeter of a rectangular field = 2\lparen l + w\rparen} \\ \text{ where l =length, and w = width} \end{gathered}

Step 2: Substitute the given data into the formula in step 1

\begin{gathered} \text{ Perimeter = 2 \lparen l + w\rparen} \\ \text{ Perimeter = 372 yards} \\ \text{ width = 87 yards} \\ \text{  372 = 2\lparen l + 87\rparen} \\ \text{ Divide both sides by 2} \\ \text{ }\frac{372}{2}\text{ = }\frac{2}{2}(l\text{ + 87\rparen} \\ 186\text{ = l + 87} \\ \text{  subtract 87 from each sides of the equation} \\ \text{ 186 - 87 = l + 87 - 87} \\ \text{  99 = l} \\ l\text{ = 99 yards} \end{gathered}

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Answer:

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Step-by-step explanation:

The y-intercept is where x is 0 (0,y)

The x-intercept is where y is 0 (x,0)

Insert 0 as the value for x to find the corresponding y value:

-5(0)-4y=10

Simplify multiplication:

0-4y=10\\\\-4y=10

Isolate the variable. Divide both sides by 4:

\frac{-4y}{4}=\frac{10}{4}  \\\\-y=\frac{10}{4} \\\\-y=\frac{5}{2}

Make the variable positive. Multiply both sides by -1:

-1(-y)=-1(\frac{5}{2})\\\\y=-\frac{5}{2}

The y-intercept is at (0,-\frac{5}{2}).

Insert 0 as the value for y to determine the value of x:

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Simplify multiplication:

-5x-0=10\\\\-5x=10

Isolate x. Divide both sides by 5:

\frac{-5x}{5} =\frac{10}{5} \\\\-x=2

Multiply both sides by -1:

-1(-x)=-1(2)\\\\x=-2

The x-intercept is at (-2,0).

:Done

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