The RAND$()$ function in Excel returns a pseudo$-$random number between $0$ and $1.$ If you enter this function into $1000$ cells $($i$.$e$.$ enter the formula in one cell and copy it to $999$ other cells$),$ approximately how many of these cells will contain values between $0\mathrm{.}1$ to $0\mathrm{.}5?$

$2.$

A project has two activities A and B that must be carried out sequentially. The probability distributions of the times required to complete each of the activities A and B are uniformly distributed in intervals $[1,6]$ and $[3,7]$ respectively. Find the total project completion time and run $6000$ simulation trials in Excel.

a$)$ What is the output of the simulations?

b$)$ What is the Excel functions would properly generate a random number for the duration of activity A in the project described above?

c$)$ What is the standard deviation of the project completion time in the project described?