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3 years ago

A rectangular

1 answer:

8 0

A = length x width

15,000 = (w + 30) x w
15,000 = $w^{2}$ + 30w
0 = $w^{2}$ + 30w - 15,000

Use quadratic formula to find that w= -15 + or - 5 $\sqrt{609}$ . Because distance cannot be negative, the width is -15 + 5 $\sqrt{609}$ meters or approximately 108.39 meters. This means that the length is approximately 138.39 meters.

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Answer:

$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

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So on this case the 95% confidence interval would be given by (563.997;741.203)

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.

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$\bar X=652.6$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=311.7 represent the sample standard deviation

n=50 represent the sample size

Soltuion to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

$652.6+2.01\frac{311.7}{\sqrt{50}}=741.203$

So on this case the 95% confidence interval would be given by (563.997;741.203)

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This is solving a system of equations

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