A sales firm receives, on average, 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive the following using the Poisson table. (a) At most 3 calls (b) At least 3 calls
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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.A bakery produces an average of 50 loaves of bread per day. The number of loaves produced by the bakery follows a Poisson distribution. What is the probability that the bakery will sell at least two loaves of bread in a day? Explain each step along with the computation.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.
- Industrial Robots are programmed to operate through microprocessors. The probability that one such computerized robot breaks down during any one 8-hour shift is 0.2. Find the probability that the robot will operate for at most five shifts before breaking down twice.Assume that three stop lights on the way to school are independent. Their time probabilities are P(Red)=0.4, P(Green)=0.5, and P(Yellow)=0.1 values. What is the probability of getting ALL THREE green lights on a trip to school?Despite all efforts by the quality control department, the fabric made at benton corporation always contains a few defects. A certain type of fabric made at this corporation contains an average of 0.51 defects per 500 yards. Using the Poisson formula, find the probability that the number of defects in a given 500-yard piece of this fabric will be between two and four.P(between 2 and 4) =
- 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.A drawer holds purple socks and yellow socks. If n socks are taken out of the drawer at random, the probability that all are yellow is 1/2. What is the smallest possible number of socks in the drawer (as a function of n)?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.) ...
- Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…Be a cafeteria with only one attendant. The rate of customer arrivals follows a Poisson process with an average of 10 customers per hour. The service time is exponentially distributed with an average time of 4 minutes. What is the probability of forming a queue, the average queue length and the average waiting time in the queue?
