You have a random variable with normal distribution .

Its density function is .

Recall that and .

And you should know that any normally distributed function can be transformed to have STANDARD normal distribution: meaning that which is great since values of standard normal distribution function are calculated and given in a table so you never have to solve the integrals above.

Here with using transformation as above will give you and .

a.

b.

c. One has to find the cutoff time T by solving the inequality . Now, leads to . Looking at the table you will find that . From here you find minutes, or rounded to nearest minute minutes.