6.(12 pts) The Grunewald Company has developed the following data regarding the rates of returnon a potential stock and the market:

State of the Economy Probability of EachRates of Return If State occurs

_________________State OccurringStock AMarket

Deep Recession.20(20%)(30%)

Mild recession.20105

Average.201520

Mild boom.202025

Strong boom.202530

a.Calculate the correlation between stock A and the market.

b.Calculate the probability that stock A's return is lower than negative 8%, that is

P (K<-8%))=?

c.Calculate the probability that stock A's return is between -8% and 15%, that is

P (-8%