Uniform Distributions $(10$ points$)[$Handwritten Fine$]$

Your firm is on a tight deadline and needs $400$ components for a new solar farm set to begin construction this week, but your regular supplier lost your order! To make it up to you, their sales rep agrees to sell you every part they produce on the assembly line for up to $1$ week. The assembly line takes between $15$ to $20$ minutes to produce each component, and runs constantly, according to a uniform distribution $($eg$.$ dunif$($x$,$ min, max$)).$ However, your contract requires you to start construction within $5$ days!

Please investigate the following:

$(5$ points$)$ Calculate the mean time to production $($mu$)$ in days for $400$ components. Calculate also the standard deviation in production time $($sigma$)$ for $400$ components.

$(5$ points$)$ On average, how many components can you expect to get within $5$ days $($mu$5)?$ How much do you expect that number to vary, on average?

Note $2\mathrm{.}1$: By vary on average, we mean Lower and Upper bounds for $1$ Standard Deviation from Mean.

Note $2\mathrm{.}2$: We will accept $(1)$ lower$5$ and upper$5$ or $(2)$ sigma$5$ from visual hint below.