For each of the following scenarios, write the desired probability in a format such as P(X = 10) and specify n and p. Do not actually compute the desired probability. If you cannot specify a numerical value for p, write in words what it represents.
a. A random sample of 1000 adults is drawn from the United States. X = the number in the sample who are living with a partner but are not married. The desired probability is the probability that at least 1/4 of the sample fits this description.
b. A pharmaceutical company claims that 20% of those taking its new allergy medication will experience drowsiness. To test this claim, it randomly assigns 500 people to take the new medication and measures X = the number who experience drowsiness. The desired probability is the probability that 110 or more people in the sample experience drowsiness if the claim is true.
c. A student has not studied the material for a 20-question true-false test and simply guesses on each question. A passing grade is 70%; the desired probability is the probability that the student passes the test.