34 and 34 I’m pretty sure
Answer:84f+57g
Step-by-step explanation:
First, multiply everything in parenthesis.
Multiply the 6 by 8f+10g, and the 4 by 3g+9f.
This gets you 48f+60g+9g-12g+36f.
After that, just solve it like normal.
You get 84f+57g.
Answer:
The 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).
Step-by-step explanation:
Let <em>X</em> = number of boards that fall outside the most rigid level of industry performance specifications.
In a random sample of 300 boards the number of defective boards was 12.
Compute the sample proportion of defective boards as follows:
![\hat p =\frac{12}{300}=0.04](https://tex.z-dn.net/?f=%5Chat%20p%20%3D%5Cfrac%7B12%7D%7B300%7D%3D0.04)
The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:
![CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D)
The critical value of <em>z</em> for 95% confidence level is,
![z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.05%2F2%7D%3Dz_%7B0.025%7D%3D1.96)
*Use a <em>z</em>-table.
Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:
![CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D%5C%5C%3D0.04%5Cpm1.96%5Csqrt%7B%5Cfrac%7B0.04%281-0.04%29%7D%7B300%7D%7D%5C%5C%3D0.04%5Cpm0.022%5C%5C%3D%280.018%2C%200.062%29%5C%5C%5Capprox%281.8%5C%25%2C%206.2%5C%25%29)
Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).
Answer:
11 and 2/3.
Step-by-step explanation:
6 and 3/12 = 72/12 + 3/12 = 75/12.
5 and 5/12 = 60/12 + 5/12 = 65/12.
75/12 + 65/12 = 140 / 12 = 70 / 6 = 35 / 3 = 11 and 2/3.
Hope this helps!