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Help solve these problems associated with Binomial probability distribution
a) A manufacturer of halogen bulbs knows that 3.5% of the production of their 100 W bulbs will be defective. What is the probability that exactly 7 bulbs in a carton of 144 bulbs will be defective?
b) A fair die has four faces numbered one to four. What is the probability of rolling a 2 exactly three times in twenty rolls of the die?
c) A packet of vegetable seeds has a germination(seeds will grow) rate of 97%. What is the probability that exactly 9 of 12 seeds planted will sprout?
d) A student take a five question multiple-choice quiz. Each question has four possible responses. The student guesses at random for each question. Calculate the probability for that if a student guesses they get exactly 5 correct.
e) There are 10 members on a committee. The probability of any member attending a randomly chosen meeting is 0.95. The committee cannot do business if more than 3 members are absent. What is the probability that 6 or more members will be present on a given date?