3. The weights of fish in a lake are normally distributed with a mean of 760 g and standard deviation . It is known that 78.87% of the fish have weights between 705 g and 815 g.
a) i. Write down the probability that a fish weighs more than 760 g
ii. Find the probability that a fish weighs less than 815 g
b) i. Write down the standardized value for 815 g
ii. Hence or otherwise, find
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
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 tiddler, find the probability that it is a salmon.