Let X represent the number of times your professor goes to the gym each week. You are given the following probability table for X. Unfortunately, your professor spilled some coffee on the probability for x = 5 and it is now illegible.
x12345 P(X = x) 0.12 0.25 0.38 0.17 ???
(a) What is P(X = 5)?(b) Find the expected value of X. (c) Find the standard deviation of X.
2. Suppose the number of mechanical failures occurring in an industrial plant follows a Poisson distribution with an average of 1.4 failures per week.
(a) What is the probability of no mechanical failures in a given week?(b) What is the probability that four or more mechanical failures will occur during a three-week period?
3. A student is preparing for an upcoming midterm exam. The professor given the student 40 practice questions and plans to select 12 of the questions at random to create the midterm exam. Suppose the student knows how to correctly answer 34 of the 40 questions. Let X represent the number of questions the student answers correctly on the exam.
(a) What is the probability distribution of X?(b) What is the probability that the student will know how to answer at least 10 questions on the exam?
4. Jed Clampett, the president of Ozark Oil, plans to conduct a preliminary survey to locate oil deposits. The probability of striking oil at a single location is 0.15, independent of all other locations.
(a) If Jed decides to drill for oil at 20 different locations, what is the probability that he will strike oil at 3 or more of those locations?