Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of $57$ hours and a standard deviation of $3\mathrm{.}5$ hours. With this information, answer the following questions.

$($a$)$ What proportion of light bulbs will last more than $62$ hours?

$($b$)$ What proportion of light bulbs will last $53$ hours or less?

$($c$)$ What proportion of light bulbs will last between $59$ and $62$ hours?

$($d$)$ What is the probability that a randomly selected light bulb lasts less than $46$ hours?

$($a$)$ The proportion of light bulbs that last more than $62$ hours is

$($Round to four decimal places as needed.$)$

$($b$)$ The proportion of light bulbs that last $53$ hours or less is $($Round to four decimal places as needed.$)$

$($c$)$ The proportion of light bulbs that lasts between $59$ and $62$ hours is $($Round to four decimal places as needed.$)$

$($d$)$ The probability that a randomly selected light bulbs lasts less than $46$ hours is $($Round to four decimal places as needed.$)$