Answer:
The lower limit is 75.04
The upper limit is 78.96
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%3D%2025)
The sample mean is ![\= x = 77](https://tex.z-dn.net/?f=%5C%3D%20%20x%20%20%3D%20%2077)
The standard deviation is ![\sigma = 5](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%205)
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%3D%20%20%28100%20%20-%2095%29%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.05)
The critical value for
obtained from the normal distribution table is
![Z_{\frac{\alpha }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%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)
=> ![E = 1.96* \frac{5 }{\sqrt{25} }](https://tex.z-dn.net/?f=E%20%3D%20%201.96%2A%20%20%5Cfrac%7B5%20%7D%7B%5Csqrt%7B25%7D%20%7D)
=> ![E = 1.96](https://tex.z-dn.net/?f=E%20%3D%201.96)
The 95% confidence interval is mathematically represented as
![\= x -E < \mu < \= x +E](https://tex.z-dn.net/?f=%5C%3D%20x%20%20-E%20%3C%20%20%5Cmu%20%3C%20%20%5C%3D%20x%20%20%2BE)
=> ![77 - 1.96 < \mu < 77 + 1.96](https://tex.z-dn.net/?f=77%20-%20%201.96%20%20%3C%20%20%5Cmu%20%3C%2077%20%2B%20%201.96)
=> ![75.04 < \mu < 78.96](https://tex.z-dn.net/?f=75.04%20%3C%20%20%5Cmu%20%3C%2078.96)
Graph needs to be labeled. I labeled it as shown on picture. It also needs a title. The title can be up to you. :) you can title it “Karen riding her bike”
Answer:
bhdwkvdveqvhjvhjawvhjcddvscg
wvvdgvewagvdgwvgdvwgevdegw
Step-by-step explanation:
1 = 51
2= 61
3= 29
Step-by-step explanation:
1) 61+68= 129
180-129= 51
2) 61 is across it so they have the same number
3) 61 +90= 151
180-151= 29
Answer:
It is an octagon if and only if it has eight sides.
Step-by-step explanation: