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Question 1: SAT scores of randomly selected samples of 12 students in university Aand 2 students in university are described i Tables University University B 472 466 484 482 482 470 482 489 492 490 473 471 469 487 486 493 470 474 476 488 494 491 a) Please fill the following table of statistical data analysis for the two universities University A University B Mean Median Mode Range Standard deviation b) For each university calculate the actual percentage of SAT scores the interval, x+3s how do your results compare the Chebyshev s rule, explain? c) Which university performs better. please explain? Question Students were asked recent survey whether they prefer meal plan (yes no) They were also asked about their acadernic degree (undergraduate, M.B Ph.D.). The survey encompassed 1030 students Their responses are documented this table: Academic degrei Undergrad M.B.A. Ph.D. Prefers meal plan 150 200 150 430 Suppose one student selected random Using this data, find the probabilities a) The student prefers meal plan? b) The student i not pursuing Ph.D. degree? c) The student prefers meal planoo pursues M.B.A degree? d) Given the student pursues undergraduate degree, the student does not prefer meal plan? c) Let be the event student prefers meal plan Let be the event that the student pursues Ph.D. degree. Are and B independent, please explain? Question 3: 3.1 Manufacturer of radios became aware that in a shipment of 20 radios to retail s store, are defective The store has policy testing random 2 radios each shipment before sale and accept shipment if both radios are not defective Whati the probability that he shipment is rejected? 3.2 Truck dealership advertises that ithas 20trucks for sale Quality inspector finds that 6 of the trucks have mechanical defects in the engine. If truck company purchases trucks random from the dealership then whati the probability that tob trucks good shape That one truck has engine failure? Question 4: Financial investor ourchases dividend funds for three years Each year independently the probability gain profit from investment is 70% and loss 30% Let X be the number of years =0, 2or the investor sustained loss, Please calculate: a) Probability distribution of x. b) Expected value of. c) Variance of X.

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Advanced Statistics Questions
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