Mathematics: When designing a study to determine this proportion, what is the minimum number of drivers you would survey to be 95% confident that the population proportion is estimated to within 0.05?

When designing a study to determine this proportion,

plutoaliko99

10.01.2022

385

Step-by-step explanation:

If the prior estimate of population proportion is unknown , then the formula to find the minimum sample size is given by :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

where, $z_{\alpha/2}$ is the z-value for significance level( $\alpha$ ) and E = the margin of error .

Given : Confidence level = 0.95

significance level : $\alpha=1-0.95=0.05$

Critical z-value for 95% confidence level : $z_{\alpha/2}=z_{0.025}=1.96$

Margin of error : E= 0.05

Also, prior population proportion is unknown.

Required sample size : $n=0.25(\dfrac{1.96}{0.05})^2$

Simplify ,

$n=384.16\approx385$

Hence,You would survey 385 drivers.

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kenziesanders01

13.10.2021

113.142857 m²

Step-by-step explanation:

As per the provide information in the given question, we have :

Radius of the circular ground = 6 m

We are asked to find the area of the ground.

Since, it is in the shape of circle, so we'll apply here the formula to find the area of the circular ground.

We know that,

>> Area of circle = πr

>> Area of the ground = $\sf \dfrac{22}{7}$ × 6 m × 6 m

>> Area of the ground = $\sf \dfrac{22}{7}$ × 36 m²

>> Area of the ground = $\sf \dfrac{792}{7}$ m²

>> Area of the ground = 113.142857 m²

$\therefore$ Therefore, area of the ground is 113.142857 m².

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