Lucresia the witch owns a magic basket and black eggs. It is observed that every minute the numbers of black eggs in the magic basket doubles. Her dark power is optimized if and only if, by 12 midnight her basket will be full of black eggs. What is the probability that she will experience optimal power when at 11:59pm her basket is half-full of black eggs?
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Lucresia the witch owns a magic basket and black eggs. It is observed that every minute the numbers of black eggs in the magic basket doubles. Her dark power is optimized if and only if, by 12 midnight her basket will be full of black eggs. What is the probability that she will experience optimal power when at 11:59pm her basket is half-full of black eggs?
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs forcustomers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4.For n = 0, 1, 2, 3, 4, the probability Pn that exactly n customers are in the shop. A. Calculate L . How would you describe the meaning of L to Newell and Jeff?B. For each of the possible values of the number of customers in the queueing system, specify howmany customers are in the queue. Then calculate Lq . How would you describe the meaning of Lq to Newelland Jeff? C.Determine the expected number of customers being served. D. Given that an average of 4 customers per hour arrive and stay to receive a haircut, determine W andWq . Describe these two quantities in terms meaningful to Newell and Jeff. E. Given that Newell and Jeff are equally fast in giving haircuts, what is the average duration of ahaircut?
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