When constructing a prependicular bisector why must the compass opening be greater than 1/2 the length of the segment ?

Mathematics

1 answer:

Tomtit [17]3 years ago

5 0

Because otherwise the two circles you build wouldn't have any intersection!

You have to draw two circles, centered at the endpoints of the segment, and connect their intersection.

If the radii are less than half the length of the circle, the circles will have no interserction.

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The manager of Petco, a nationwide chain of pet supply stores, wants to study characteristics of the customers, particularly the

shutvik [7]

Answer:

The 95% confidence interval would be given by (19.141;23.538)

Step-by-step explanation:

1) 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".

$\bar X=21.34$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9.22 represent the sample standard deviation

n=70 represent the sample size

2) Confidence interval

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:

$df=n-1=70-1=69$

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(0.025,69)".And we see that $t_{\alpha/2}=1.994$