Step 1:
\The standard deviation of the weights of certain machine components σ is 0.09 gr.
\Sample mean is µ = 8.3 gr.
\I am assuming that the mean the top and bottom is 3 %. \ \ so
\Z for 3 % confidence interval is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=79e5ce3641c2ed1f1bdc0fa7569a5c00.png\")
and the top is 1.88. \ \
Let the values of the weights be x gr.
\x = µ + zσ
\The bottom number is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=f159bd3decbffbde73ba387bc47cc4f7.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4be3614391809e822a91f1d2a8bffd4c.png\")
Thus, x = 8.1308 lbs is the weight that separates the bottom 3 %.
\\
The top number is x = 8.3 + 1.88(0.09).
\ ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e05f05511f55c1dfbee86663bec17e60.png\")
Thus, x = 8.4692 lbs is the weight that separates the top 3 %.
\Solution:
\The weight that separates the bottom 3 % is 8.1308 lbs.
\The weight that separates the top 3 % is 8.4692 lbs.
\