A component is known to have an exponential time$-$to$-$failure distribution with a mean life of $10,000$ hours. The probability of the component lasting at least $8000$ hours is

In a helical spring manufacturing industry, the spring wire diameter have process mean of $10mm$ and process standard deviation of $0\mathrm{.}4mm.$ If the samples of size $4$ are randomly selected from the process, then the $2$ control limits for the wire diameter is