The probability distribution of X, the number of seats occupied in a jeepney at a given time of day, is given by 1 2 3 4 5 7 8 10 f(x) .02 .06 .07 .12 .20 .20 .14 .08 .07 .03 .01 Find the probability that the number of occupied seats are at most seven.
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- for a publisher of technical books, the probability that any page contains at least one error is p = .005. Assume the errors are independent from page to page. What is the approximate probability that one of the 1,000 books published this week will contain at most 3 pages with errors?The time it takes a mechanic to change the oil on a car is uniformly distributed between 11 and 30 minutes. The rectangle with area 1 below depicts this. The area of the shaded rectangle is the probability that a mechanic finishes the oil change between 20.19 minutes and 27.68 minutes. Find the area of the shaded rectangle. Round your answer to 4 decimal places (if possible).At a bank, there is a line of 3 people and only one cashier that serves one person at a time. The time that the cashier takes to serve each person has an exponential distribution with a mean of 5 minutes. Calculate the probability that the total time of serving the 3 people is less than 15 minutes. Assume that the serving times are independent.
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- You have a uniform distribution whose lowest value is 7 and whose highest value is 15. Find the probability that a randomly selected number from this distribution will be between 9.3 and 10.6.Suppose we played roulette x5 times (where x = 3 is the last digit of your student ID) and each time we bet on the number 17. In each game, xthe probability of winning is 1/37. Calculate the probability P(X = z), where z is the second-to-last digit of your student ID (in this case, z = 5). Draw the probability distribution function graph for the given scenario. Also, calculate the probability of winning less than 5 timesDo this task in R commander.Suppose the average tread-life of a certain brand of tire is 45,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life between 30,000 and 50,000 miles?