A lazy professor gave two tests A and B to a class of n students and assignedmarks A; and B;, respectively, to student i, for iand independently at random with values from the set of possible gradesk. For example, the values of grades could be chosen from1,2,..., n, uniformly1,2,...А+, А, А-, В+, В, В-,С+,С, С-, D+, D.D-, F,in which case k13. Derive a formula for the probability that some studentreceives the same grade in both tests. Is it likely that this could happenin the present the Distributed Computing class which has n = 91 studentsregistered, for k = 13?

Given: n students appear for 2 tests namely, A and B and scores of any student i ( where i=…

Answered: A lazy professor gave two tests A and B…

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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A multiple-choice test consists of 9 questions. Each question has answer choices of a, b, c, and d, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that he gets at least 3 of them correct? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)
sen? 2. A poker hand consists of 5 cards chosen at random from a standard deck of cards. How many poker hands containing all face cards are possible? 3. Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected? a. 5 people regardless of gender b. 3 females and 2 males c. at least 3 females d. 4 females and 1 male e. 5 females 4. In a game of poker, a full house is a combination of 5 cards chosen from a standard deck of cards with three of a kind and two of a kind. How many full houses are possible?
Q.no.4 The test scores on the same algebra test were recorded for nine students randomly selected from a classroom taught by teacher A and eight students randomly selected from a classroom taught by Teacher B. Teacher A: 65, 88, 93, 95, 80, 76, 79, 77.Teacher B: 91, 85, 70, 82, 92, 68, 86, 87, 75. Test the hypothesis that the difference in the average scores for students taught by these two teachers equal to zero. Use 5% level of significance.
. Suppose an exam consists of multiple-choice questions, with each question having 5 options. Exactlyone of the five options is the correct answer. Suppose 24 points are awarded for a correctly answeredquestion.(a) How many points should be deducted for an incorrectly answered question, so that for a studentguessing randomly, the expected score on a question is zero?(b) If a student is able to correctly eliminate one option as a possible correct answer but is still guessingrandomly, what happens to his/her expected score for that question? Use your answer to (a) asthe number of points being deducted for an incorrect answer.
Q1) Below find the records of 12 randomly selected used pickup trucks (none used commercially) and 11 randomly selected used passenger cars, the time (in years) that they were kept by the original owner before being sold: Used pickup trucks | 3 | 2.5 2.9 5 4.2 3.1 3.3 4 5.3 3.8 4.5 Used passenger cars | 2.2 3 2.8 4.3 4 3.3 2.9 2.1 2 3.1 3 It is known that the standard deviation of used pickup trucks is 2 years and of used passenger cars is 1 year. (a) Investigate, at the 5% significant level, whether the mean time (in years) that used pickup trucks were kept by the original owner before sold is larger than used passenger cars. (b) What assumption is needed to perform the test in (a). (c) Construct the 96% confidence interval for the mean difference of time (in years) were kept by the original owner before sold between used passenger cars and used pickup trucks. Use this confidence interval to tell whether there is difference in the mean time (in years) between these 2 tynes of…
A deck consists of 32 cards with 2 suits labelled A and B, and numbered ranks from 1 to 16. That is, there are 16 cards of each suit and 2 cards of each rank. A single card is chosen at random from the deck. What is the probability of it being rank 7 given that it is suit b? And What is the probability of it being suit b given that it has rank 7?
A multiple-choice test consists of 6 questions. Each question has answer choices of a, b, c, and d, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that he gets at most 2 of them correct? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)
For a binomial experiment with n trials, let p = probability of success, q = probability of failure, and x = number of successes in n trials. Which of the following statements is %3D correct? Op+q= 1 Ox
you are given the following set P of 9 sets p= (1,1), (1,2),(1,3),(2,1),(2,2),(3,1),(3,2),(3,3).if two different points are randomly selected, what is the probability that the midpoint of these two selected points will also belong to set P??
B) Are males or females do a better job of detecting cheating? Justify your answer using conditions needed to justify your answer .
Please help me
Q1. Given B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, -1), v3 = (1, 4, –1, 2), v4 = (6, 9, 4, 2)} %3! %3D B' = {wi = (0, 8, 8), w2 = (-7,8, 1), w3 = (-6,9, 1)} -2 1 6 2 1 -3 0 7 1 A = 1 and T : R4 → R3 such that matrix A is the transformation matrix in relation to B and B' basis. a)Verify that set B is a basis of R*and that the set B' is a basis of R³. b)Find [T(v1)]B, [T(v2)]B [T(v3)]B, [T(v4)]B c) find T(v1), T(v2), T(v3), T(v4)

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