Answer:
![\mu_{\hat{p}}=0.19](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%7Bp%7D%7D%3D0.19)
![\sigma_{\hat{p}}=0.0785](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%7Bp%7D%7D%3D0.0785)
Step-by-step explanation:
We know that the mean and the standard error of the sampling distribution of the sample proportions will be :-
![\mu_{\hat{p}}=p](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%7Bp%7D%7D%3Dp)
![\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%7Bp%7D%7D%3D%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
, where p=population proportion and n= sample size.
Given : The proportion of students at a college who have GPA higher than 3.5 is 19%.
i.e. p= 19%=0.19
The for sample size n= 25
The mean and the standard error of the sampling distribution of the sample proportions will be :-
![\mu_{\hat{p}}=0.19](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%7Bp%7D%7D%3D0.19)
![\sigma_{\hat{p}}=\sqrt{\dfrac{0.19(1-0.19)}{25}}\\\\=\sqrt{0.006156}=0.0784601809837\approx0.0785](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%7Bp%7D%7D%3D%5Csqrt%7B%5Cdfrac%7B0.19%281-0.19%29%7D%7B25%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B0.006156%7D%3D0.0784601809837%5Capprox0.0785)
Hence , the mean and the standard error of the sampling distribution of the sample proportions :
![\mu_{\hat{p}}=0.19](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%7Bp%7D%7D%3D0.19)
![\sigma_{\hat{p}}=0.0785](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%7Bp%7D%7D%3D0.0785)
The slope is 2 because remember, y= mx+b
m= slope
the slope is always multiplied by x
We need to find out how much is worth one yard in both fabrics, so we divide $15.00 by 2 and $37.50 by 5:
$15.00 ÷ 2 = $7.50 per yard
$37.50 ÷ 5 = $7.50 per yard
As both prices per yard are the same, the answer is: <span>Yes, these fabrics have the same unit cost.</span>
18. You can do this in a calculator. 26 - 8 = 18. v = 18.