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

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

The margin of error is of:

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

35% of junior executives left their company within three years.

This means that $\pi = 0.35$

0.95 = 95% confidence level

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

To update this study, how many junior executives should be surveyed?

Within 3% of the proportion, which means that this is n for which M = 0.03. So

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

$0.03 = 1.96\sqrt{\frac{0.35*0.65}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.35*0.65}$

$\sqrt{n} = \frac{1.96\sqrt{0.35*0.65}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.35*0.65}}{0.03})^2$

$n = 971.2$

Rounding up:

972 junior executives should be surveyed.

5 0

3 years ago

an angle measures 58.4° more than the measure of its supplementary angle what is the measure of each angle

olga55 [171]

Answer:

58.4

119.2

Step-by-step explanation:

Givens

Let one angle = x

Let the other angle = x + 58.4

Together they make 180 degrees.

Equation

x + x + 58.4 = 180 Collect like terms.

Solution

2x + 58.4 = 180 Subtract 58.4 from both sides

2x = 180 - 58.4

2x = 121.6 Divide by 2

x = 60.8

Answer

x = 60.8

x + 58.4 = 119.2

8 0

3 years ago

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