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 .
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.