n a chemical pro cess, the amount of a certain

typ e of impurity in the output is di$$cult to control

and is thus a random variable. Sp eculation is that the

p opulation mean amount of the impurity is $0\mathrm{.}20$ gram

p er gram of output. It is known that the standard

deviation is $0\mathrm{.}1$ gram p er gram. An exp eriment is con$-$ducted to gain more insight regarding the sp eculation

that $=0\mathrm{.}2.$ The pro cess is run on a lab scale $50$

times and the sample average $$ x turns out to b e $0\mathrm{.}23$

gram p er gram. Comment on the sp eculation that the

mean amount of impurity is $0\mathrm{.}20$ gram p er gram. Make

use of the Central Limit Theorem in your work.