Learning Materials
Features
Discover
Chapter 5: Q 5.151. (page 242)
Explain the significance of binomial coefficients with respect to Bernoulli trials.
The number of outcomes that have exactly x number of successes in Bernoulli trials is defined as the Binomial Coefficients.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Archery. An archer shoots an arrow into a square target 6 feet on a side whose center we call the origin. The outcome of this random experiment is the point in the target hit by the arrow. The archer scores 10 points if she hits the bull's eye-a disk of radius 1 foot centered at the origin; she scores 5 points if she hits the ring with inner radius 1 foot and outer radius 2 feet centered at the origin; and she scores 0 points otherwise. Assume that the archer will actually hit the target and is equally likely to hit any portion of the target. For one arrow shot, let S be the score.
(a) Obtain and interpret the probability distribution of the random variable S. (Hint: The area of a square is the square of its side length; the area of a disk is the square of its radius times.)
(b) Use the special addition rule and the probability distribution obtained in part (a) to determine and interpret the probability of each of the following events:
Craps. The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2,3 , or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that the probability is 0.493 that a player wins a game of craps. Suppose we consider a win by a player to be a success,
a. Identify the success probability,
b. Construct a table showing the possible win-lose results and their probabilities for three games of craps. Round each probability to three decimal places.
c. Draw a tree diagram for part (b).
d. List the outcomes in which the player wins exactly two out of three times.
e. Determine the probability of each of the outcomes in part (d). Explain why those probabilities are equal.
f. Find the probability that the player wins exactly two out of three times.
g. Without using the binomial probability formula, obtain the probability distribution of the random variable , the number of times out of three that the player wins.
h. Identify the probability distribution in part (g).
World series. The World series in baseball is won by the first team to win four games ( ignoring the 1903 and 19919 - 1921 World series, when it was a best of nine). From the document World series history on the baseball Almanac website. as of November 2013, the length of the world series are as given in the following table.
Let X denote the number of games that it take to complete a world series, and let Y denote the number of games that it took to complete a randomly selected world series from among those considered in the table.
Part (a) Determine the mean and standard deviation of the random variable Y. Interpret your resuts.
Part (b) Provide an estimate for the mean and standard deviation of the random variable X. Explain your reasoning
In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.
Part (a) Find the mean of the random variable.
Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.
ASU Enrollment Summary. According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University ( ASU ) in the Fall 2012 semester, by class level, is as shown in the following table. Here , 1 = freshman , 2 = sophomore , 3 = junior , and 4 = senior.
| Class level | 1 | 2 | 3 | 4 |
| No. of students | 9,652 | 11,115 | 17,302 | 21,114 |
Let X denote the class level of a randomly selected ASU undergraduate.
(a) What are the possible values of the random variable X?
(b) Use random-variable notation to represent the event that the student selected is a junior ( class - level 3 ).
(c) Determine P ( X = 3 ), and interpret your answer in terms of percentages.
(d) Determine the probability distribution of the random variable X.
(e) Construct a probability histogram for the random variable X.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine