Two statistics post-grad students went fishing at a lake during a break at a conference in England. Beforehand they agreed that the one who caught the more impressive fish would have their dinner paid for by the other. Anna caught a 40 cm long perch, whilst Joe caught a 42 cm bream.

-From long term studies of the fish populations in the lake, it is known that the length of perch is approximately normally distributed with mean of 29.6 cm and standard deviation of 9.5 cm.

The length of bream is approximately normally distributed with mean of 38.4 cm and standard deviation of 4.2 cm.

The next day Joe went fishing again and caught 1 bream and 1 perch. Use the formula for the difference of random variables to find the probability that the bream is longer than the perch. What assumption was made to do this calculation?