Suppose that the test score of a student taking the final of a probability course is a random variable with mean 85.(a) Give an upper bound for the probability (in three decimal places) that the student's test score will exceed 95.Suppose that we know, in addition, that the standard deviation of the student's test score on the final is 8.7.(b) What is a lower bound of the probability (in three decimal places) that the student will score between 75 and 95 ?SC

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Answered: Suppose that the test score of a…

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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The average student loan debt for college graduates is $25,750. Suppose that that distribution is normal and that the standard deviation is $10,350. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar. Find the probability that the college graduate has between $22,700 and $30,000 in student loan debt. (------) The middle 20% of college graduates' loan debt lies between what two numbers? Low: $(______) High: $(_____)
2
For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 500 and a standard deviation of 170. The grading process of this year's exam has just begun. The average score of the 35exams graded so far is 512. What is the probability that a sample of 35 exams will have a mean score of 512 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Suppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)
For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 515 and a standard deviation of 170. The grading process of this years exam has just begun. The average score of the 40 exams graded so far is 490. What is the probability that a sample of 40 exams will have a mean score of 490 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)
For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 515 and a standard deviation of 175. The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 518. What is the probability that a sample of 40 exams will have a mean score of 518 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. Sub Continue
Suppose that the only information you have is that in the last 90 days a total of 27,000 students visited. Can you say anything about the probability that more than 500 students visit on a given day? Suppose that you got some additional information saying that the standard deviation of students visiting per day is 50 students. Can you say anything more precise about the probability that more than 500 students visit on a given day?
Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 131000 dollars. Assume the standard deviation is 30000 dollars. Suppose you take a simple random sample of 83 graduates.Find the probability that a single randomly selected salary is at least 129000 dollars.P(X > 129000) = Find the probability that a sample of size n=83n=83 is randomly selected with a mean that is at least 129000 dollars.P(M > 129000) = Enter your answers as numbers accurate to 4 decimal place
Suppose collection of all quiz marks of a class of students is normally distributed with a mean of 7 and a standard deviation of 1. Calculate the probability that a student will receive a mark less than 5.
Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% want a used copy. Consider randomly selecting 15 purchasers. In USE SALT (a) What are the mean value and standard deviation of the number who want a new copy of the book? (Round your standard deviation to two decimal places.) mean students standard deviation students (b) What is the probability that the number who want new copies is more than two standard deviations away from the mean value? (Round your answer to three decimal places.) (c) The bookstore has 10 new copies and 10 used copies in stock. If 15 people come in one by one to purchase this text, what is the probability that all 15 will get the type of book they want from current stock? [Hint: Let X = the number who want a new copy. For what values of X will all 15 get what they want?] (Round your answer to three decimal places.) (d) Suppose that new copies cost $110 and used copies cost $80.…
Suppose that the duration of a particular type of criminal trial is known to have a mean of 18 days and a standard deviation of 6 days. We randomly sample 9 trials.Give the distribution of ΣX.Find the probability that the total length of the 9 trials is more than 188 days. 70 percent of the total of 9 of these types of trials will last more than how long? (Round your answer to two decimal places.)days

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