math

[Maximum mark: 16] The weights of fish in a lake are normally distributed with a mean of 760g and standard deviation o. It is known that 78.87% of the fish have weights between 705 g and 815g. (a) (1) Write down the probability that a fish weighs more than 760g. (ii) Find the probability that a fish weighs less than 815 g. (b) (1) Write down the standardized value for 815 g. (ii) Hence or otherwise, find o . A fishing contest takes place in the lake. Small fish, called tiddlers, are thrown back into the lake. The maximum weight of a tiddler is 1.5 standard deviations below the mean. (c) Find the maximum weight of a tiddler. 12 (d) A fish is caught at random. Find the probability that it is a tiddler. (e) 25% of the fish in the lake are salmon. 10% of the salmon are tiddlers. Given that a fish caught at random is a fiddler, find the probability that it is a salmon. 14)