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▪Anything written in hand and any answers calculated besides Python will get zero points.

▪If your Python codes do not work in a certain question but your answer is correct, you would receive zero for that question since it would be considered cheating.

▪Submit your Python codes and results to the “assignment” section in Modules on Canvas. Please show the answers to each question below the Python codes.

▪The due date is 11:59 PM on August 1 (Thursday), 2024.

1. The probability distribution function of xisfx (x) = 0.2, 1 < x  < 6.

a) Find P(2 < x < 5).

b) Find P(x > 4).

c) Find F(3).

d) Find the 80th percentile.

2. The lifetime of a certain brand of lightbulb has the following distribution (in hours).

a) Find the probability that a randomly selected lightbulb of this kind lasts 700 to 900 hours.

b) Find the probability that a randomly selected lightbulb of this kind lasts longer than 850 hours.

c) Find the 80th percentile of the lifetime of this kind lightbulb.

3. a) A shipment of 25 compact discs contains 5 defective ones. Ten are selected at random. What is the probability that two of them will be defective?

b) In a college classroom, some chairs are designed for left-handers. Suppose this classroom has

20 chairs, and 8 of them are made for lefties. If 5 students randomly select chairs and sit on them in this classroom, what is the probability that at least 4 of those selected will be seats for lefties?

4. David didn’t study for his Introduction to Logic exam, consisting of 15 true-false questions. He did blind guessing on each question.

a) If he needs to score 10 or more correct to pass, what is the probability that he will fail the exam?

b) Find the probability that he correctly answers 6 to 11 (inclusive) questions.

5. Thirty percent of the automobiles in a certain city are foreign-made. Four cars are selected at random. Let x be the number of foreign-made cars sampled. Let “success” be a case in which a foreign-made automobile is selected with a probability of success of 0.3.

a) Find P(x = 3).

b) Find P(x ≥ 3).

c) Find P(1 ≤ x ≤ 4).

d) Find P(x < 2).