$1.$ Suppose in a software testing environment, $71\%$ of all software programs are reported to pass all test cases on their first run. If a sample of $10$ new software programs is randomly selected, find:

a$)$ The probability that exactly $4$ programs will pass all test cases on their first run $[3$ marks$]$

b$)$ The probability that at least $9$ programs will pass all test cases on their first run $[4$ marks$]$

c$)$ Find the mean $($rounded to $3$ decimal places$)[1$ mark$]$

d$)$ Find the standard deviation $($rounded to $3$ decimal places$)[1$ mark$]$