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3 years ago

Plz help me with this

Mathematics

1 answer:

Greeley [361]3 years ago

3 0

Answer: $\bold{b)\quad \dfrac{x-5}{8}}$

<u>Step-by-step explanation:</u>

$y=8x+5\\\\\\\text{Swap the x's and y's. Then solve for y:}\\x=8y+5\\\\\\\text{Subtract 5 from both sides:}\\x-5=8y\\\\\\\text{Divide both sides by 8:}\\\dfrac{x-5}{8}=y$

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In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha

Afina-wow [57]

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

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.

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

In which

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For this problem, we have that:

$\pi = 0.21$

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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 $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

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

$0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}$