In a printing shop, print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to arrival times. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. A particular printer in this shop is capable of printing five pages per minute. The average request results in ten printed pages of poster. (i)There are currently five jobs in the queue – one active and four waiting to be processed. A new customer submit a job to this printer and it becomes the sixth job in the queue. Calculate the probability that he will have to wait more than 5 minutes for the printer to begin processing his job. Assume that the time between consecutive jobs in the queue is negligible. (ii) Name the alternative distribution of the random variable that you are considering in (i)

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which the pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to  20  samples of rat skin. Four skins were analyzed at each of the time intervals  1 ,   2 ,   4 ,   10 ,  and  24  hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table.   Duration   Amounts Absorbed 1   1.3 1.4 1.3 2.1 2   1.6 2.0 1.3 2.0 4   1.9 1.6 2.1 1.7 10   2.0 2.1 2.0 1.7 24   2.4 2.2 2.6 2.2 Can you conclude that the amount in the skin varies with time? Use the  =α0.001  level of…

The Escherichia coli culture (better known as E. coli) doubles every 40 minutes. If 30 E. coli are present initially, what will the number of E. coli be after 3 hours?

The total daily net operating time of Car Max Company is 8 hr/day. The company observes a 20 minutes lunch, 20 minutes break, 10 minutes briefing, and 10 minutes maintenance check daily. Calculate the Takt time (seconds/unit) if the company has a 20days/month working calendar, and the total daily customer demand (Td) of 18,000/month.

Suppose customers arrive to a single server at the rate of 1/2 customers per minute. The capacity of the server is 1/3 customers per minute. Both service time and interarrival times are assumed to be exponential. Suppose the system is initially empty. As the system unfolds, its inventory (in process and waiting) will: (a) reach a long-run average of 3 customers (b) reach a long-run average of 2 customers (c) stay in the system an average of 6 minutes (d) grows unboundedly in the long-run (e) None of the above

A machine has three components but can remain functional if at least two are working. Suppose that the failure times are exponential with means 2 months, 1 month, and 4 months, respectively for each component. What is the aver: ge length of time the machine can remain functional?

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which a pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to  20  samples of rat skin. Four skins were analyzed at each of the time intervals  1 ,  2 ,  4 ,  10 , and  24  hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table.   Duration Amounts Absorbed 1 1.8 1.9 1.8 2.2 2 1.5 2.4 1.5 2.5 4 1.5 2.7 1.3 1.9 10 1.3 1.5 1.4 2.6 24 1.8 1.3 2.3 1.8   Construct an ANOVA table. Round your answers to four decimal places. One-way ANOVA: Pesticide Amount…

A doctor prescribes 100 milligrams of a therapeutic drug that decays by about 20% eachhour (ie. after 1 hour, 20% of the drug is gone). Assume the quantity of the drug is modeled by anexponential equation. What is the half-life of the drug? Please use a calculator to compute the finalanswer and round down to two decimal places.

Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?

If a city's population is 1.3 million now and will grow at a continuous rate of 4.5% in the future, what will the city's population be in the year 2030? Give your answer in millions of people with two places of accuracy to the right of the decimal.