Answer:
The diameter is: 8 feet
The radius is: 4 ft.
The area is: 50.27
Step-by-step explanation:
Hope this helps!
Answer:
![P(\hat p>0.14)](https://tex.z-dn.net/?f=%20P%28%5Chat%20p%3E0.14%29)
And using the z score given by:
![z = \frac{\hat p -\mu_p}{\sigma_p}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B%5Chat%20p%20-%5Cmu_p%7D%7B%5Csigma_p%7D)
Where:
![\mu_{\hat p} = 0.12](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%20%3D%200.12)
![\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%20%5Csqrt%7B%5Cfrac%7B0.12%2A%281-0.12%29%7D%7B474%7D%7D%3D%200.0149)
If we find the z score for
we got:
![z = \frac{0.14-0.12}{0.0149}= 1.340](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B0.14-0.12%7D%7B0.0149%7D%3D%201.340)
So we want to find this probability:
![P(z>1.340)](https://tex.z-dn.net/?f=%20P%28z%3E1.340%29)
And using the complement rule and the normal standard distribution and excel we got:
![P(Z>1.340) = 1-P(Z](https://tex.z-dn.net/?f=%20P%28Z%3E1.340%29%20%3D%201-P%28Z%3C1.340%29%20%3D%201-0.9099%3D%200.0901)
Step-by-step explanation:
For this case we have the proportion of interest given
. And we have a sample size selected n = 474
The distribution of
is given by:
![\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})](https://tex.z-dn.net/?f=%20%5Chat%20p%20%5Csim%20N%20%28p%20%2C%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%29%20)
We want to find this probability:
![P(\hat p>0.14)](https://tex.z-dn.net/?f=%20P%28%5Chat%20p%3E0.14%29)
And using the z score given by:
![z = \frac{\hat p -\mu_p}{\sigma_p}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B%5Chat%20p%20-%5Cmu_p%7D%7B%5Csigma_p%7D)
Where:
![\mu_{\hat p} = 0.12](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%20%3D%200.12)
![\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%20%5Csqrt%7B%5Cfrac%7B0.12%2A%281-0.12%29%7D%7B474%7D%7D%3D%200.0149)
If we find the z score for
we got:
![z = \frac{0.14-0.12}{0.0149}= 1.340](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B0.14-0.12%7D%7B0.0149%7D%3D%201.340)
So we want to find this probability:
![P(z>1.340)](https://tex.z-dn.net/?f=%20P%28z%3E1.340%29)
And using the complement rule and the normal standard distribution and excel we got:
![P(Z>1.340) = 1-P(Z](https://tex.z-dn.net/?f=%20P%28Z%3E1.340%29%20%3D%201-P%28Z%3C1.340%29%20%3D%201-0.9099%3D%200.0901)
Sheila will add 8 ounces of yellow paint to the mixture