Standard deviation of a normal model from a lower-tail probability, an interval within a multiple of the standard deviation and a conditional probability

The lengths of adult fish of one species in a reservoir are normally distributed with mean \(41.8\) cm, correct to three significant figures. Of these fish, \(85\%\) have lengths between \(33\) cm and \(48\) cm, and the probability that a fish is shorter than \(33\) cm is \(0.04\).

1. Find the probability that a fish of this species is longer than \(48\) cm.[2]
2. 1. Find the standardised value, \(z\), that corresponds to a length of \(33\) cm.
   2. Hence find the standard deviation of the lengths.[4]

A fish is classed as standard size when its length is within \(1.2\) standard deviations of the mean.

3. 1. Find the range of lengths of the fish that are classed as standard size.
   2. One fish is caught at random. Find the probability that it is standard size.[5]

Of the fish of this species in the reservoir, \(40\%\) are female, and \(65\%\) of the female fish are standard size.

4. A fish caught at random is standard size. Find the probability that it is female.[4]