In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two differentlots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient tofill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, theviscosity of batches consisting of two or more lots of material is more difficult to control, and 40% ofsuch batches require additional processing to achieve the required viscosity. Let A denote the event thata batch is formed from two different lots, and let B denote the event that a lot requires additionalprocessing. Determine the following probabilities:а. Р(А)e. P(ANB)f. P(ANB')g. P(B)b. P(А)С. Р[ВА)d. P(B|A')

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Answered: In the manufacturing of a chemical…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1. Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores follow test scoresS group 7 46 86 629 5 5 3 4 4 7 2 2 2 471 2 1 5 5 1) constant sound 2) random sound 3) no sound
2. Measurements were taken for entropy and enthalpy changes for many salts under a variety of water + methanol of NaCl (table salt) for several concentrations of methanol. Four independent conditions. The following table presents the results for enthalpy of transfer (in kJ/mol) from water to measurements were made at each concentration. Concentration (%) Enthalpy 1.62 1.60 1.62 1.66 5 10 20 30 2.69 2.66 2.72 2.73 3.56 3.45 3.65 3.52 3.35 3.18 3.40 3.06 a. Construct an ANOVA table in Excel. (8 points) b. Is it plausible that the enthalpy is the same at all concentrations? Explain. (4 points) No, brause the value is very low c. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for concentrations 5 and 30. Show your work. (12 points) d. Compute the quantity s = √MSE, the estimate of the standard deviation σ. (2 points)
_) Jane bakes sourdough loaves, which are full of gluten. Unfortunately, John is allergic to gluten and wants to bake gluten-free loaves. John does not have their own “starter” (a mix of yeast, flour, and water that makes a loaf rise in the oven). Jane's starter is 50g of water and 50g of flour with gluten, and a microscopic amount of yeast that we will ignore. Jane gives John 50g of her starter. For John's first loaf, they replace the missing half of their starter with 25 g of gluten-free flour and 25g of water. This means their starter is now 25g of gluten-free flour, 25g of flour with gluten, and 50g of water. Once the yeast in this starter is fully activated, John is ready to make their first loaf. To bake the loaf they mix 50 g (half) of the starter with 225g of gluten-free flour and 225g of water, meaning the loaf is always
I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy. E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density function given by. f(t)=(at^2 0=t=50, b(100-t) 50=t=100, 0 elsewhere) i) Show that a = 3/312500 and b= 3/6250 ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km. iii)Sketch the graph of T on the axes below, clearly labelling the scale. iv) Find the expected value and variance of brand E car tyres. v) Find the probability that the lifetime of brand E car tyres lies within two standard…
3.3 4.manufactures 37-in. high def LCD tvs in 2 separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of tvs to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the 2 TMA plants to the 2 Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $7 $3 Location II $8 $9 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x,y)= What is the minimum cost? 6.Solve the linear programming problem by…

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