A local laboratory is attempting to validate a new test and agrees to exchange 7 specimens with a Reference Laboratory. Afterwards, all 7 of the local laboratory's results were higher in value than those of the Reference Laboratory.

a.Assuming only chance differences in test methodology between the two laboratories [i.e., the local laboratory's test results are equally likely to be bigger or smaller than Reference results, or the number of higher results is a random variable X ~ B(n=7, p=0.5)] and no ties, what is the exact probability of the exchange outcome?

b.Suppose the two laboratories exchanged 70 specimens. What is the approximate probability of 45 or more higher test results by the local laboratory compared to Reference if only chance differences in test methodologies exist?

This problem has me confused. Can someone please assist me and show their work step by step? Thank you.