The diameters D of screws made in a factory are normally distributed with

mean $1$mm$.$ Given that $10\%$ of the screws have diameters greater than

$1\mathrm{.}04$mm$,$ find the standard deviation correct to $3$ significant figures, and hence

show that about $2\mathrm{.}7\%$ of the screws have diameters greater than $1\mathrm{.}06$mm$.$

Find, correct to $2$ significant figures,

$($i$)$ the number d for which $99\%$ of the screws have diameters that exceed d mm

$($ii$)$ the number e for which $99\%$ of the screws have diameters that do not

differ from the mean by more than e mm