We are learning to calculate the probability of sums and difference of random numbers.
Here is the problem: One athlete knows from past experience that the distances of his javelin throws follow a normal distribution with mean 60 (units) and standard deviation 6 (units). The distances of his hammer throws follow a normal distribution with mean 54 (units) and standard deviation 4 (units). The athlete's performances in the two events are independent.
I know how to calculate probability if his next javelin throw is smaller/greater than hammer throw. I can calculate probability of both javelin/hammer throw is greater or smaller than some distance.
But how to calculate the probability that events (javelin throw and hammer throw) can have same value?
to solve the we are using z test with the statistics table for z values.
*I also changed values if you want you can change again.