Question Solved1 Answer A balanced coin is tossed three times. Let Y equal the number of heads observed. (a) Use the formula for the binomial probability distribution to calculate the probabilities associated with Y = 0, 1, 2, and 3. PCY - 0) = P(Y = 1) = P(Y = 2) = P(Y = 3) - (b) Construct the probability distribution below. y ply) 0 1 2 3 (c) Find the expected value and standard deviation of Y, using the formulas E(Y) = np and ViY) = npg. (Round your answers to three decimal places.) u = (d) Using the probability distribution from part (b), find the fraction of the population measurements lying within 1 standard deviation of the mean. How do your results compare with the results of Tchebysheff's theorem and the empirical rule? This is consistent with the empirical rule. This is consistent with Tchebysheff's theorem. This is consistent with the empirical rule and Tchebysheff's theorem. This is not consistent with either the empirical rule or Tchebysheff's theorem. Using the probability distribution from part (b), find the fraction of the population measurements lying within 2 standard deviations of the mean. How do your results compare with the results of Tchebysheff's theorem and the empirical rule? This is consistent with the empirical rule. This is consistent with Tchebysheff's theorem. This is consistent with the empirical rule and Tchebysheff's theorem. This is not consistent with either the empirical rule or Tchebysheff's theorem.

3) Write a Monte-Carlo simulation to test your analytical result in part 2 using poissrnd, binornd, and normrnd with the appropriate parameter Vary the number of trials from 100 to 100000 (in steps of ~10,000) and report the error in the computed probability.2) Your zero-g-proof-pen manufacturing company is in dire straights, and you want to know what the 3) Write a Monte-Carlo simulation to test your analytical result in part 2 using poissrnd, binornd, and normrnd with the appropriate parameter Vary the number of trials from 100 to 100000 (in steps of ~10,000) and report the error in the computed probability.2) Your zero-g-proof-pen manufacturing company is in dire straights, and you want to know what the probability is that you will have to declare bankruptcy. In order to stay afloat, you need the following three things to happen: Your factory needs to fill an order for 500 pens without making any defective pens (assume a binomial distribution with a 0.05% chance of error), you also need a space shuttle to be launched in the next month (consider space shuttle launch per month a Poisson random variable with rate 0.4, and you need exactly 1 launch), and you need your CEO to find at least 3 NASA secretaries who will take his phone calls (in the past this occurrence has been normally distributed with mean 2.6 and variance 1). Assuming that these three events are independent, what is the probability that your company will go under? 4

The effect of temperature on the rate of a reaction was studied and the following data obtained: k (s¹) T (°C) 7.98x10-4 9 1.16x10-3 14 1.79x10-3 20 2.54x10-3 25 4.93×10-3 35 7.64x10-3 42 1.23x10-² 50 1.47x10-2 53 It is known that the variation of the rate constant k with the absolute temperature T is described by the Arrhenius equation: k = A exp [(-E₂ The effect of temperature on the rate of a reaction was studied and the following data obtained: k (s¹) T (°C) 7.98x10-4 9 1.16x10-3 14 1.79x10-3 20 2.54x10-3 25 4.93×10-3 35 7.64x10-3 42 1.23x10-² 50 1.47x10-2 53 It is known that the variation of the rate constant k with the absolute temperature T is described by the Arrhenius equation: k = A exp [(-E₂ )/(RT)] where E, is the activation energy, R is the universal gas constant and A is the pre-exponential factor (units of the rate constant). Taking the natural logarithm of both sides affords: Ea In k = In A- RT For a plot of y = Ink versus x = 1/T, calculate the slope of the best straight line using linear regression.

Choi Company manufactures two skin care lotions, Smooth Skin and Silken Skin, from a joint process. The joint costs incurred are \( \$ 410,000 \) for a standard production run that generates 290,000 pints of Smooth Skin and 130,000 pints of Silken Skin. Smooth Skin sells for \( \$ 2.50 \) per pint, while Silken Skin sells for \( \$ 4.00 \) per pint. Choi Company manufactures two skin care lotions, Smooth Skin and Silken Skin, from a joint process. The joint costs incurred are \( \$ 410,000 \) for a standard production run that generates 290,000 pints of Smooth Skin and 130,000 pints of Silken Skin. Smooth Skin sells for \( \$ 2.50 \) per pint, while Silken Skin sells for \( \$ 4.00 \) per pint. Requlred: 1. Assuming that both products are sold at the split-off point, how much of the joint cost of each production run is allocated to Smooth Skin using the relative sales value method? 2. If no separable costs are incurred after the split-off point, how much of the joint cost of each production run is allocated to Silken Skin using the physical measure method? 3. If separable processing costs beyond the split-off point are \( \$ 1.60 \) per pint for Smooth Skin and \( \$ 1.30 \) per pint for Silken Skin, how much of the joint cost of each production run is allocated to Silken Skin using a net realizable value method? 4. If separable processing costs beyond the split-off point are \( \$ 1.60 \) per pint for Smooth Skin and \( \$ 1.30 \) per pint for Silken Skin, how much of the joint cost of each production run is allocated to Smooth Skin using a physical measure method? (For all requlrements, do not round Intermedlate calculations. Round flnel answers to nearest whole doller amounts.)

Please write your answer in python Define a function called sasquatch(), which has one parameter. Name the parameter whatever you want The function should print the value of its parameter to the console. Additional Notes: Regarding your code's standard output, CodeLab will check for case errors and will check whitespace (tabs, spaces, newlines) exactly.

The initial mass of a certain species of fish is 2 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 4/yr. However, commercial fishing removes fish mass at a constant rate of 11 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be?

The initial mass of a certain species of fish is 2 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 5/yr. However, commercial fishing removes fish mass at a constant rate of 12 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? When will all the fish be gone? Inco The fish will all be gone in years. (Round to three decimal places as needed.)