Answer
a)13.35%, yes.
b)160.195 and 189.805
Work Step by Step
a)$z=\frac{value-mean}{standard \ deviation}=\frac{185-175}{9}=1.11$ Using the table the probability is 1 minus the probability belonging to 1.11, hence: P=1-0.8665=0.1335=13.35%. This is not that close to 0, hence a significant amount will be lost.
b)By using the table, the z-score corresponding to 0.05 and 0.95: z=$\pm 1.645$. Hence the corresponding values:$mean+z⋅standard \ deviation=175-1.645⋅9=160.195.$
$mean+z⋅standard \ deviation=175+1.645⋅9=189.805.$
