Following are the calculation to the value:
Given:
[tex]n= 20\\\\\mu= 105\\\\\sigma= 15\\\\CI= 99.5\%\\\\[/tex]
To find:
value=?
Solution:
[tex]\to z= 2.807 for 99.5\%\\\\\to 2.807=\frac{x-105}{\frac{15}{\sqrt{20}}}\\\\\to 2.807 \times\frac{15}{\sqrt{20}} =x-105\\\\\to 2.807 \times\frac{15}{\sqrt{20}}+105 =x\\\\\to x= \to 2.807 \times\frac{15}{\sqrt{20}}+105\\\\[/tex]
Solving the value for x\\\\
[tex]\to x= 114.41\\\\[/tex]
Therefore, the final answer is "114.41".
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