Problem $1.(2/20$ points$)$ Suppose that we wish to predict whether a given stock will issue a dividend this year $($Yes$$ or $$No$)$ based on X$,$ last year$$s percent profit. We examine a large number of companies and discover that the mean value of X for companies that issued a dividend was $$X $=10,$ while the mean for those that didn$$t was $$X $=0.$ In addition, the variance of X for these two sets of companies was $$$2=36.$ Finally, $80\%$ of companies issued dividends. Assuming that X follows a normal distribution, predict the probability that a company will issue a dividend this year given that its percentage profit was X $=4$ last year