You really struggle remembering to bring your lunch to work. Each day seems to be independent as to whether you remember to bring your lunch or not. The chance that you forget your lunch each day is 22.8%.

Consider the next 42 days. Let $\displaystyle {X}$ be the number of days that you forget your lunch out of the 42 days. Calculate the following:
(a)


$\displaystyle \mu_{{X}}$:

$\displaystyle \sigma_{{X}}$:



(b) What would be the first unusually large number of days to forget your lunch? Use the range rule of thumb. (Enter a whole number.)

(c) Find the probability of forgetting your lunch at least as many times as your answer to part (b). Find the exact answer; don't use the range rule.