a) The general notation is: X∼Bin(40,0.85)
b) P(X=35) would describe the probability of the antibiotic being effective for 35 people.
c) This describes P(X is greater than or equal to 35). Thus you must find:
P(X is greater than or equal to 35) = P(X=35) + P(X=36) + P(X=37) + P(X=38) + P(X=39) + P(X=40) = (40/35)(0.85)^35(0.15)^5 +…+ (4040)(0.85)^40(0.15)^0.
d) Half the patients is 20. So less than 20 is 19. Hence, here it describes P(X

Question

a)  The general notation is: X∼Bin(40,0.85)
b)  P(X=35) would describe the probability of the antibiotic being effective for 35 people. 
c) This describes P(X is greater than or equal to 35). Thus you must find:
P(X is greater than or equal to 35) = P(X=35) + P(X=36) + P(X=37) + P(X=38) + P(X=39) + P(X=40) = (40/35)(0.85)^35(0.15)^5 +…+ (4040)(0.85)^40(0.15)^0.
d) Half the patients is 20. So less than 20 is 19. Hence, here it describes P(X<20)=P(X is lesser than or equal to 19).