Stats/std dev problem help please

I am finding this question impossible, can someone help me please? Thanks


The University of New South Wales Library checks out an average of 2534 books per day, with a standard deviation of 378 books per day. Assuming that the distribution of books checked out per day is well approximated by a normal distribution, determine (to 4 dec pl)
1. the probability that on any given day, the number of books checked out exceeds 2300
2. the probability that the average daily lending activity over a three month (i.e. 90 day) period is less than 2500 books or more than 3000 books per day.

Let X = number of books checked out per day
X~normal(2534 , 378^2)

P(number of books checked out exceed 2300)
= P(X > 2300)
= P(Z > (2300 - 2534) / 378)
= P(Z > -0.619047619)
= 1 - P(Z <= -0.619047619)
= 1 - P(Z >= 0.619047619)
= 1 - 0.2676
= 0.7324

Let Y = average number of books checked out in 90 days
Y~normal(2534 , (378)^2 / 90)

P(average lending activity in 90 days is less than 2500 books or more than 3000 books)
= P(Y < 2500) + P(Y > 3000)
= P(Z < (2500 - 2534) / (378 / sqrt(90))) + P(Z > (3000 - 2534) / (378 / sqrt(90)))
= P(Z < -0.853313019) + P(Z > 11.69540785)
= P(Z >= 0.853313019) + 0
= 0.1977