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3 years ago

What is the equation of (4,10),(6,11) in standard form?

Mathematics

1 answer:

SIZIF [17.4K]3 years ago

7 0

ANSWER

The standard form is:

$x - 2y = - 16$

EXPLANATION

The given line passes through (4,10)and (6,11).

The slope of this line is

$m = \frac{11 - 10}{6 - 4}$

$m = \frac{1}{2}$

The equation is given by the formula,

$y-y_1=m(x-x_1)$

We plug in the first point and the slope to get.

$y-10= \frac{1}{2} (x-4)$

$2y - 20 = x - 4$

$x - 2y = - 20 + 4$

$x - 2y = - 16$

The standard form is

$x - 2y = - 16$

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

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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.

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".

$\bar X=652.6$ 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 $t_{\alpha/2}=2.01$