Answer:
(221.39, 300.61) and (255.2223, 266.7777)
Step-by-step explanation:
Given that X, the lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days and a standard deviation of 17 days
Middle 98% would lie on either side of the mean with probability ±2.33 in the std normal distribution on either side of 0
Corresponding we have x scores as
Between
and ![261+2.33*17](https://tex.z-dn.net/?f=261%2B2.33%2A17)
i.e. in the interval = (221.39, 300.61)
If sample size = 47, then std error of sample would be
![\frac{17}{\sqrt{47} }](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B%5Csqrt%7B47%7D%20%7D)
So 98% of pregnancies would lie between
and ![262+2.33*\frac{17}{\sqrt{47} }](https://tex.z-dn.net/?f=262%2B2.33%2A%5Cfrac%7B17%7D%7B%5Csqrt%7B47%7D%20%7D)
= (255.2223, 266.7777)
No it does not. when solved you should get y=3/x, meaning it shows inverse variation.
Firstly, foil -(k + 1/4) (think of the minus sign as -1):
![\frac{2}{3}k-k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7Dk-k-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B12%7Dk%2B%5Cfrac%7B4%7D%7B12%7D%20)
Next, combine like terms:
![-\frac{1}{3}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B3%7Dk-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B12%7Dk%2B%5Cfrac%7B4%7D%7B12%7D%20)
Next, we have to add 1/3k on both sides, but first we have to find the LCD, or lowest common denominator, of 3 and 12. To do this, list the multiples of both and the lowest one they share is their LCD. In this case, the LCD is 12. Multiply both sides of -1/3 by 4/4 and 1/12 by 1/1:
![-\frac{1}{3}\times \frac{4}{4}=-\frac{4}{12}\\\\\frac{1}{12}\times \frac{1}{1}=\frac{1}{12}\\\\-\frac{4}{12}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B3%7D%5Ctimes%20%5Cfrac%7B4%7D%7B4%7D%3D-%5Cfrac%7B4%7D%7B12%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7B12%7D%5Ctimes%20%5Cfrac%7B1%7D%7B1%7D%3D%5Cfrac%7B1%7D%7B12%7D%5C%5C%5C%5C-%5Cfrac%7B4%7D%7B12%7Dk-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B12%7Dk%2B%5Cfrac%7B4%7D%7B12%7D%20)
<em>Now</em> add 4/12k on both sides of the equation:
![-\frac{1}{4}=\frac{5}{12}k+\frac{4}{12}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B5%7D%7B12%7Dk%2B%5Cfrac%7B4%7D%7B12%7D%20)
Next, to subtract 4/12 on both sides we need to find the LCD of 4 and 12. It's the similar process as we did with 12 and 3. This time the LCD is also 12. Multiply both sides of -1/4 by 3/3 and 4/12 by 1/1:
![-\frac{1}{4}\times \frac{3}{3}=-\frac{3}{12}\\\\\frac{4}{12}\times \frac{1}{1}=\frac{4}{12}\\\\-\frac{3}{12}=\frac{5}{12}k+\frac{4}{12}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B3%7D%7B3%7D%3D-%5Cfrac%7B3%7D%7B12%7D%5C%5C%5C%5C%5Cfrac%7B4%7D%7B12%7D%5Ctimes%20%5Cfrac%7B1%7D%7B1%7D%3D%5Cfrac%7B4%7D%7B12%7D%5C%5C%5C%5C-%5Cfrac%7B3%7D%7B12%7D%3D%5Cfrac%7B5%7D%7B12%7Dk%2B%5Cfrac%7B4%7D%7B12%7D%20)
<em>Now</em> subtract 4/12 on both sides:
![-\frac{7}{12}=\frac{5}{12}k](https://tex.z-dn.net/?f=%20-%5Cfrac%7B7%7D%7B12%7D%3D%5Cfrac%7B5%7D%7B12%7Dk%20)
Lastly, multiply both sides by 12/5, and <u>your answer will be:</u>
![-\frac{84}{60}=-\frac{7}{5}=k](https://tex.z-dn.net/?f=%20-%5Cfrac%7B84%7D%7B60%7D%3D-%5Cfrac%7B7%7D%7B5%7D%3Dk%20)