Answer:
The probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
![\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
The sample size is, <em>n</em> = 553 > 30. Thus, the Central limit theorem is applicable in this case.
Compute the mean and standard deviation as follows:
![\mu_{\hat p}=p=0.04\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.04\times 0.96}{553}}=0.0083](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp%3D0.04%5C%5C%5C%5C%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.04%5Ctimes%200.96%7D%7B553%7D%7D%3D0.0083)
Compute the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% as follows:
![P(\hat p>0.05)=P(\frac{\hat p-\mu_{\hat p}}{\sigm_{\hat p}}>\frac{0.05-0.04}{0.0083})\\\\=P(Z>1.20)\\\\=1-P(Z](https://tex.z-dn.net/?f=P%28%5Chat%20p%3E0.05%29%3DP%28%5Cfrac%7B%5Chat%20p-%5Cmu_%7B%5Chat%20p%7D%7D%7B%5Csigm_%7B%5Chat%20p%7D%7D%3E%5Cfrac%7B0.05-0.04%7D%7B0.0083%7D%29%5C%5C%5C%5C%3DP%28Z%3E1.20%29%5C%5C%5C%5C%3D1-P%28Z%3C1.20%29%5C%5C%5C%5C%3D1-0.88493%5C%5C%5C%5C%3D0.11507%5C%5C%5C%5C%5Capprox%200.1151)
Thus, the probability that the proportion of airborne viruses in a sample of 553 viruses would be greater than 5% is 0.1151.
1. -4a-6=-12
add 6 to both sides
-4a-6+6=-12+6
-4a=-6
Divide by -4
![a= \frac{6}{4} = 1 \frac{1}{2}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7B6%7D%7B4%7D%20%3D%201%20%5Cfrac%7B1%7D%7B2%7D%20)
2.
![\frac{3}{5} z- \frac{1}{4} = \frac{17}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20z-%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B17%7D%7B20%7D%20)
add
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20)
to both sides but you will need to make a common denominator on the right
![\frac{3}{5} z- \frac{1}{4} + \frac{1}{4} = \frac{17}{20} + \frac{5}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20z-%20%5Cfrac%7B1%7D%7B4%7D%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%20%5Cfrac%7B17%7D%7B20%7D%20%2B%20%20%5Cfrac%7B5%7D%7B20%7D%20)
![\frac{3}{5}z= \frac{11}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7Dz%3D%20%20%5Cfrac%7B11%7D%7B10%7D%20%20%20)
Divide by
![\frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20)
which means multiply by the <span>reciprocal</span>.
![\frac{3}{5}* \frac{5}{3} z= \frac{11}{10} * \frac{5}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%2A%20%5Cfrac%7B5%7D%7B3%7D%20z%3D%20%5Cfrac%7B11%7D%7B10%7D%20%2A%20%5Cfrac%7B5%7D%7B3%7D%20%20)
![z= \frac{55}{30} =1 \frac{5}{6}](https://tex.z-dn.net/?f=z%3D%20%5Cfrac%7B55%7D%7B30%7D%20%3D1%20%5Cfrac%7B5%7D%7B6%7D%20)
3.
![2 \frac{1}{2}(e-1 \frac{3}{4})=5 \frac{1}{2}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B2%7D%28e-1%20%5Cfrac%7B3%7D%7B4%7D%29%3D5%20%5Cfrac%7B1%7D%7B2%7D%20%20%20)
Distribute
![2 \frac{1}{2} e-4 \frac{3}{8} =5 \frac{1}{2}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B2%7D%20e-4%20%5Cfrac%7B3%7D%7B8%7D%20%3D5%20%5Cfrac%7B1%7D%7B2%7D%20)
Subtract
![2 \frac{1}{2} e=1 \frac{1}{8}](https://tex.z-dn.net/?f=2%20%5Cfrac%7B1%7D%7B2%7D%20e%3D1%20%5Cfrac%7B1%7D%7B8%7D%20)
Divide
![e= \frac{9}{20}](https://tex.z-dn.net/?f=e%3D%20%5Cfrac%7B9%7D%7B20%7D%20)
4. 3w+7=20
Subtract
3w=13
Divide
![w= \frac{13}{3} = 4 \frac{1}{3}](https://tex.z-dn.net/?f=w%3D%20%5Cfrac%7B13%7D%7B3%7D%20%3D%204%20%5Cfrac%7B1%7D%7B3%7D%20)
5. -.2p+.4=-1.2
Subtract
-.2p=-1.6
Divide
p=8
6.
![\frac{y}{4} - \frac{3}{5} = \frac{18}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7By%7D%7B4%7D%20-%20%5Cfrac%7B3%7D%7B5%7D%20%3D%20%5Cfrac%7B18%7D%7B20%7D%20)
Add, made sure you change to common denominator first
![\frac{y}{4} = 1 \frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7By%7D%7B4%7D%20%3D%201%20%5Cfrac%7B1%7D%7B4%7D%20)
Multiply by 4
y=5
Hope that helps
what is the question can you out it in ?
Answer:
=4.9
Step-by-step explanation:
3.4-(-1.5)
+
3.4+1.5=4.9
Answer:
-2a^4+8a^3-6a^2
Step-by-step explanation:
2a^2(a-1)(3-a)
2a^2(-a^2 +3a-3+a)
2a^2(-a^2+4a-3)
-2a^4+8a^3-6a^2