Answer:
a) The 90% confidence interval for the mean noise level at such locations
(112.46 , 163.54)
b) The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
Step-by-step explanation:
<u><em>Step(i)</em></u> :-
Noise levels at 3 airports were measured in decibels yielding the following data
108 146 160
Mean of given data
![x^{-} = \frac{108+146+160}{3} = 138](https://tex.z-dn.net/?f=x%5E%7B-%7D%20%3D%20%5Cfrac%7B108%2B146%2B160%7D%7B3%7D%20%3D%20138)
x : 108 146 160
x-x⁻ : -30 8 22
(x-x⁻ )² : 900 64 484
Variance σ ² = ∑(x-x⁻ )²/ n-1
= ![\frac{900+64+484}{3-1}= 724](https://tex.z-dn.net/?f=%5Cfrac%7B900%2B64%2B484%7D%7B3-1%7D%3D%20724)
Standard deviation
σ = √724 = 26.90
<u><em>Step(ii):</em></u>-
The 90% confidence interval for the mean noise level at such locations
![(x^{-} - Z_{0.90} \frac{S.D}{\sqrt{n} } , (x^{-} + Z_{0.90} \frac{S.D}{\sqrt{n} } )](https://tex.z-dn.net/?f=%28x%5E%7B-%7D%20-%20Z_%7B0.90%7D%20%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%2C%20%28x%5E%7B-%7D%20%2B%20Z_%7B0.90%7D%20%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%29)
The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
![(138 - 1.645 \frac{26.90}{\sqrt{3} } , (138 + 1.645 \frac{26.90}{\sqrt{3} } )](https://tex.z-dn.net/?f=%28138%20-%201.645%20%5Cfrac%7B26.90%7D%7B%5Csqrt%7B3%7D%20%7D%20%2C%20%28138%20%2B%201.645%20%5Cfrac%7B26.90%7D%7B%5Csqrt%7B3%7D%20%7D%20%29)
( 138 - 25.54 , 138 + 25.54 )
(112.46 , 163.54)
Answer:
ASA
Step-by-step explanation:
We have congruent side, the congruent angle and another congruent angle = 90 degrees. Both angles are adjacent to one side/.ASA
Let William be x years old.
Thomas = (4 + x) years
In five years,
William = (x + 5) years
Thomas = 4 + x + 5 = (9 + x) years
Given, in five years sum of their ages is 24.
x + 5 + 9 + x = 24
2x + 14 = 24
2x = 24 - 14
2x = 10
x =
![\frac{10}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B2%7D%20)
x = 5
Hence, William is 5 years old and Thomas is 9 years old.
Answer:
836m
Step-by-step explanation: