\textbf{A: receive a merit B: hour \textless{} 90}  \textbf{P(B) = P(hour \textless{} 90) = P(Z\textless(90-80)/7) = 0.9236}  \textbf{P(A) = 0.2}  \textbf{P(hour \textgreater{} x) = 0.2}  \textbf{P(hour ≤ x) = 0.8}  \textbf{P(Z ≤ (x-80)/7) =0.8}  \textbf{P(A∩B) = P(x\textless hour\textless90) = P($$\frac{x-80}{7} \textless{} Z \textless{} \frac{90-80}{7}$$) = P($$Z \textless{} \frac{90-80}{7}$$) - P($$Z \textless{} \frac{x-80}{7}$$) = 0.9236-0.8 = 0.1236}  \textbf{P(A\textbar B) = $$\frac{P(A∩B)}{P(B)}$$ = $$\frac{0.1236}{0.9236}$$=0.134} 
\textbf{The distribution of the number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90?} 
a: $$0.077$$ 
b: $$0.123$$ 
c: $$0.134$$ 
d: $$0.618$$ 
e: $$0.923$$ 