Assuming the length of nails in a large box of 3-inch nails is normally distributed with mean of 3 with standard deviation of 0.02, find the following:

(round all answers to four decimal places)

1) What is the probability that a randomly selected nail from the box is longer than 3.025 inches?

2) What is the probability that a randomly selected nail from the box is between 2.99 and 3.01 inches?

3) If the manufacturer intends to discard the bottom 5% and the top 5% of nails, in terms of their lengths, what would be the cut-off lengths for nails to be discarded?

low-end:

high-end: