A vending machine in a supermarket breaks down an average of four times per month. Using the Poisson probability distribution formula, find the probability that during the next month this machine will have (a) Exactly two breakdowns (b) At most one breakdown
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- Given that the switch board of a consultant's office receives on the average 0.6 call per minute, find the probability that (a) In a given minute there will be at least one call. (b) In a 4-minute interval, there will be at least 3 calls.Complaints about an Internet brokerage firm occur at a rate of 4 per day. The number of complaints appears to be Poisson distributed. A. Find the probability that the firm receives 5 or more complaints in a day. Probability = B. Find the probability that the firm receives 10 or more complaints in a 3-day period. Probability =The probability that a randomly chosen sales prospect will make a purchase is 20%. What is the probability (to three decimal places) that the salesperson will make four or more sales if six sales calls are made on a given day?
- The switchboard in a Minneapolis law office gets an average of 3 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. What is the probability that the office receivesa. exactly 4 calls at noon on Monday. b. exactly 8 calls at noon on Monday.A survey finds that customers are charged incorrectly for 7 out of every 30 items, on average. Suppose a customer purchases 11 items. Find the following probability. A customer is not charged incorrectly for any item.A workshop tows in an average of five damaged cars per week. Find the probability that exactly 20 cars are towed in a four-week period. * 0.098 0.176 0.089 0.560
- 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?A washing machine in a laundromat breaks down an average three times per month. Using the Poisson probability formula find the probability that during the next month, it will break at most once. а. .1992 O b. .5432 c. .6754 d. .2240
- Suppose a baseball player's batting average is .325. What is the probability that in the next 100 times at bat he will get at most 30 hits?40% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. The probability is (Round to three decimal places as needed.) ...Birds arrive at a feeding table independently, at an average rate of six per hour. Find the probability that two birds will arrive in the next ten minutes.