Answer:
-3.4(2.7a-1.7)-1.2a= 47.3
A = -4
The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days.
That is,
Consider X be the length of the pregnancy
Mean and standard deviation of the length of the pregnancy.
Mean 
Standard deviation \sigma =15
For part (a) , to find the probability of a pregnancy lasting 308 days or longer:
That is, to find 
Using normal distribution,



Thus 
So 




Thus the probability of a pregnancy lasting 308 days or longer is given by 0.00256.
This the answer for part(a): 0.00256
For part(b), to find the length that separates premature babies from those who are not premature.
Given that the length of pregnancy is in the lowest 3%.
The z-value for the lowest of 3% is -1.8808
Then 
This implies 
Thus the babies who are born on or before 238 days are considered to be premature.
Answer:
x=1+√334, x=1−√334
Step-by-step explanation:
Answer:
![-\frac{3}{8} +\frac{\sqrt[]{23}i }{8},-\frac{3}{8} -\frac{\sqrt[]{23}i }{8}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B8%7D%20%2B%5Cfrac%7B%5Csqrt%5B%5D%7B23%7Di%20%7D%7B8%7D%2C-%5Cfrac%7B3%7D%7B8%7D%20-%5Cfrac%7B%5Csqrt%5B%5D%7B23%7Di%20%7D%7B8%7D)
or

Step-by-step explanation:

Bring the 8 to the left side so that we equal the equation to 0. To do this, simply substract 8 on both sides.

Where;

![Formula: x=\frac{-b\frac{+}{}\sqrt[]{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=Formula%3A%20x%3D%5Cfrac%7B-b%5Cfrac%7B%2B%7D%7B%7D%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%20%20%7D%7B2a%7D)
Replace. Let x be r
![r=\frac{-3\frac{+}{}\sqrt[]{(3)^2-4(4)(2)} }{2(4)}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-3%5Cfrac%7B%2B%7D%7B%7D%5Csqrt%5B%5D%7B%283%29%5E2-4%284%29%282%29%7D%20%20%7D%7B2%284%29%7D)
![r=\frac{-3\frac{+}{}\sqrt[]{9-32} }{8}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-3%5Cfrac%7B%2B%7D%7B%7D%5Csqrt%5B%5D%7B9-32%7D%20%20%7D%7B8%7D)
![r=\frac{-3\frac{+}{}\sqrt[]{-23} }{8}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-3%5Cfrac%7B%2B%7D%7B%7D%5Csqrt%5B%5D%7B-23%7D%20%20%7D%7B8%7D)
It has no real solution because the square root is negative.
We can say that,
![r=-\frac{3}{8} \frac{+}{}\frac{\sqrt[]{23}*\sqrt[]{-1} }{8}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B3%7D%7B8%7D%20%5Cfrac%7B%2B%7D%7B%7D%5Cfrac%7B%5Csqrt%5B%5D%7B23%7D%2A%5Csqrt%5B%5D%7B-1%7D%20%20%7D%7B8%7D)
![r=-\frac{3}{8} \frac{+}{}\frac{\sqrt[]{23}i }{8}](https://tex.z-dn.net/?f=r%3D-%5Cfrac%7B3%7D%7B8%7D%20%5Cfrac%7B%2B%7D%7B%7D%5Cfrac%7B%5Csqrt%5B%5D%7B23%7Di%20%7D%7B8%7D)
