In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. Let A denote the event that a batch is formed from two different lots, and let B denote the event that a lot requires additional processing. 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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- There are three types of contaminants that spoils water. Organic pollutants (O), volatile solvents (V), and chlorinated compounds (C). A new analytical method to detect (D) contaminants in water is being tested. The makers of the test claim that it can detect high levels of organic pollutants with 98% accuracy, volatile solvents with 99% accuracy, and chlorinated components with 89% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 65% of them are contaminated with organic pollutants, 20% with volatile solvents, and 15% with traces of chlorinated compounds. A test sample is selected randomly. (a) What is the probability that the test will signal? (b) If the test signals, what the probability that volatile solvents are present? (c) If the test does not signal, what is the probability that chlorinated compounds are present? Note: Use the notations in the brackets to describe the events.Balls, Inc. produces two products, Squid Balls (S) and Fish Balls (F), in two departments, the Mixing Department and Deep Frying Department. Production of the two products (combined) during any period cannot exceed 23,700 kilos. Data on the two products follow: Squid Balls (S) Fish Balls (F) Total time available (minutes) Contribution margin per kilo P40 30 TIME REQUIRED (Minutes) Mixing (M) 3.0 1.5 48,000 Which of the following is not a constraint function for this linear programming problem? a. 3S+ 1.5F 48,000 c. S+ F≤ 23,700 b. 2S+ 3.6F ≤ 72,000 d. CM = 40S + 30F Deep Frying (D) 2.0 3.6 72,000We want to test the relative efficacy of a new cholesterol lowering drug A versus existing drug B. We randomize nĄ subjects with high cholesterol to take treatment A and ng subjects to take treatment B. After a l-month followup, we measure cholesterol levels in both groups. Suppose the data in the two groups are independent and YA,Y;ª,..., YA N(µA, o²) and YB,YB,.., Y,B iid N(µB,0²), where o? = 9 is known. Let Y4 and YB be the sample average cholesterol level in group A and B. 1. What is the distribution of the difference in sample means:  =Ÿª-ŸB? Hint: what is the distribution of each group's sample average? What do we know about linear combinations of normal RVs? 2. Let A = µA - µB be the true difference in cholesterol levels in populations treated with Â-A A versus B. What is the distribution of Z = ? Vo2/na+o²/ng 3. Suppose YA = 20 and YB = 26 with na = nB = 36. Conduct an a = .05 significance level test of Ho : A = 0 versus Ha : A # 0. Do you reject or fail to reject the null at…
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- 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…A study measures the absorption rate of three different types of organic chemical solvents. These solvents are used to clean industrial fabricated-metal parts and are potentially hazardous. The organic chemical solvents are Aromatics, Chloroalkanes and Esters. Aromatics ChloroalkanEsters es 0.95 1.58 0.43 1.15 0.91 0.61 0.82 0.83 0.34 1.05 1.16 0.60 0.57 0.53 1.45 Test if there is a significance difference in the mean absorption rate for the three solvents? Use a = 0.05.5. The compressive strength of concrete (in kg/m) is being tested b y two civil engineers. The first engineer tests ten specimens and obtains the following data: 2000 2100 2050 2150 2200 2050 2000 2100 2250 2000 While the following data is obtained by the second engineer who tests eight specimens: 2000 2200 2050 2150 2250 2100 2250 2150 The compressive strength of concrete is assumed to be normally distributed. Construct a 90% confidence interval for the ratio of standard deviation of compressive strength of all concretes.[(0.505,1.757) [ref:T2S20708] 6. A new teaching method to improve the failing rate if English SPM papers is being considered. The existing and new teaching method were applied to samples of students so as to determine whether the new teaching method improves the proportion of students who failed in their English papers. 1425 of 1500 students who were taught based on the existing teaching method and 1920 of 2000 students who were taught based on the new teaching method…