Mathematics, 06.03.2020 22:42 mjmckay03

The widths of 79 randomly selected window blinds were found to have a standard deviation of 2.37. Construct the 95% confidence interval for the population standard deviation of the widths of all window blinds in this factory. Round your answers to two decimal places.

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Answer from: sg3635939

$\frac{(78)(2.37)^2}{104.316} \leq \sigma^2 \leq \frac{(78)(2.37)^2}{55.466}$

$4.254 \leq \sigma^2 \leq 8.000$

And for the deviation we just need to take the square root of the variance and we got:

$2.06 \leq \sigma^2 \leq 2.83$

Step-by-step explanation:

Data given and notation

s=2.37 represent the sample standard deviation

$\bar x$ represent the sample mean

n=79 the sample size

Confidence=95% or 0.95

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=79-1=78

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 values.

The excel commands would be: "=CHISQ.INV(0.025,78)" "=CHISQ.INV(0.975,78)". so for this case the critical values are:

$\chi^2_{\alpha/2}=104.316$

$\chi^2_{1- \alpha/2}=55.466$

And replacing into the formula for the interval we got:

$\frac{(78)(2.37)^2}{104.316} \leq \sigma^2 \leq \frac{(78)(2.37)^2}{55.466}$

$4.254 \leq \sigma^2 \leq 8.000$

And for the deviation we just need to take the square root of the variance and we got:

$2.06 \leq \sigma^2 \leq 2.83$

Answer from: Quest

You have 2 sides that are 2 cms and you have 6 sides that are 1/2 cm and you have 4 sides that are 1 cm. the smallest sides are 1/2 the medium sized sides are 1 and the smallest are 1/2. so to find the perimeter you have to add them all up together so your answer will be 11 cm's

Answer from: Quest

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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