$($c$)$ A reliability test was conducted on a sample of $5000$ similar components

at a fixed temperature. The number of survivors at the end of the $500$th

hour was $4950,$ and at the end of the $1000$th hour was $4920.$ Calculate the

average failure rate $(\%/1000$ hr$.)$ over

$[$i$]$ The first $500-$hour

$[$ii$]$ The second $500-$hour period.

$($d$)$ From the result obtained in $($c$),$ state the reason and the region of the

bath$-$tub curve which can be said to follow this failure rate pattern.