The height of female students are normally distributed with mean 160 cm and standard deviation 8 cm.

(i)Find the probability that a random selected female student has a height greater than 170 cm.

(ii)Find the probability that a random selected female student has a height greater than 150 cm.

(iii)Find the probability that a random selected female student has a height between 140 and 150 cm.

(iv)Any female students whose height is greater than 170 cm is defined as tall. An adult female student is chosen at random. Given that she is tall, find the probability that she has a height greater than 180 cm.

(v)Half of tall female students have a height greater than k cm. Find the value of k.

(vi)Calculate the minimum height that 99% of the students would be expected to be.