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3 years ago

Need help with fill in the exponent #9

Mathematics

1 answer:

kkurt [141]3 years ago

3 0

When you raise something to the power of -1, all that happens is that thing turns upside down.

For example: (x^3 / y^4)^-1 will become (y^4 / y^3), basically the same fraction but just swap the numerator and denominator.

In your example, the first exponent is 4 and the second exponent is 3.

Answer: y^4 and x^3

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You must survey 784 air passengers.

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In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

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z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

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$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

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So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Assume that nothing is known about the percentage of passengers who prefer aisle seats.

This means that $\pi = 0.5$ , which is when the largest sample size will be needed.

Within 3.5 percentage points of the true population percentage.

We have to find n for which M = 0.035. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.035 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.035\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.035}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.035})^2$

$n = 784$

You must survey 784 air passengers.

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2 years ago