Answer:
The 95% confidence interval is ![295.9 < \mu< 324.1](https://tex.z-dn.net/?f=295.9%20%3C%20%5Cmu%3C%20324.1)
A 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval
Step-by-step explanation:
From the question we are told that
The sample size is ![n = 25](https://tex.z-dn.net/?f=n%20%20%3D%20%2025)
The mean is ![\= x = 310 \ mg](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%20310%20%5C%20mg)
The standard deviation is ![\sigma = 36 \ mg](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%2036%20%5C%20mg)
Given that the confidence level is 95% then the level of significance is mathematically represented as
![\alpha = 100 - 95](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20100%20-%2095)
=> ![\alpha = 5\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%205%5C%25)
=> ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
Next we obtain the critical value of
from the normal distribution table , the value is
![Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3DZ_%7B%5Cfrac%7B0.05%20%7D%7B2%7D%20%7D%20%20%3D%20%201.96)
Generally the margin of error is mathematically represented as
![E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }](https://tex.z-dn.net/?f=E%20%3D%20%20Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%2A%20%20%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%20%7D)
substituting values
![E = 1.96 * \frac{36 }{\sqrt{25} }](https://tex.z-dn.net/?f=E%20%3D%20%201.96%20%2A%20%20%5Cfrac%7B36%20%7D%7B%5Csqrt%7B25%7D%20%7D)
![E = 14.1](https://tex.z-dn.net/?f=E%20%3D%2014.1)
The 95% level of confidence interval is mathematically represented as
![\= x - E < \mu](https://tex.z-dn.net/?f=%5C%3D%20x%20-%20E%20%3C%20%5Cmu%3C%5C%20%5C%3D%20x%20-%20E)
substituting values
![310- 14.1 < \mu< 310+ 14.1](https://tex.z-dn.net/?f=310-%2014.1%20%3C%20%5Cmu%3C%20310%2B%2014.1)
![295.9 < \mu< 324.1](https://tex.z-dn.net/?f=295.9%20%3C%20%5Cmu%3C%20324.1)
The 95% level of confidence mean that there is 95% chance that the true population mean will be in this interval
Answer:
z=3
Step-by-step explanation:
2(2z -4)=4
Divide by 2
2/2(2z -4)=4/2
2z-4 = 2
Add 4 to each side
2z-4+4 = 2+4
2z = 6
Divide by 2
2z/2 = 6/2
z=3
Answer:
20 dollars
Step-by-step explanation:
I think 20+20+20=60 then 60-40=20
Answer:8
Step-by-step explanation:
You find the average which is adding them all together then dividing by how many numbers you added.
-20 because 40 is a positive and spent is negative