Hiya! So statistics is definitely not my strongest subject haha. Need some help with this! I can't seem to work the 75% and 25% into the solution.

This is the full question:

In a genetics experiment involving fruit flies, you know that 25% of flies are normal and 75% of flies are mutants (have a condition). Normal flies have thorax lengths (X) that are normally distributed with mean 1.3mm and standard deviation 0.1mm. Mutant flies have thorax lengths (Y ) that are normally distributed with mean 1.0mm and standard deviation 0.15mm.


(a) What is the probability that a mutant fly is correctly classified as a mutant?
(b) What is the probability that a normal fly is correctly classified as normal?
(c) What is the probability that a mutant fly is incorrectly classified as a normal?
(d) If you have classified 10,000 flies, how many of those would you expect to be mutant flies incorrectly classified as a normal?
(e) Suppose you want to choose a cutoff such that 95% of the mutant flies are classified correctly. What cutoff would you use?

Any help would be greatly appreciated.