Statistics: The Art and Science of Learning from Data (4th Edition)

4th Edition

ISBN: 9780321997838

Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg

Publisher: PEARSON

See similar textbooks

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Videos

Textbook Question

Chapter 6, Problem 86CP

Longest streak made In basketball, when the probability of making a free throw is 0.50 and successive shots are independent, the probability distribution of the longest streak of shots made has μ = 4 for 25 shots, μ = 5 for 50 shots, μ = 6 for 100 shots, and μ = 7 for 200 shots.

a. How does the mean change for each doubling of the number of shots taken? Interpret.
b. What would you expect for the mean of the longest number of consecutive shots made in a sequence of (i) 400 shots and (ii) 3200 shots?
c. For a long sequence of shots, the probability distribution of the longest streak is approximately bell shaped and σ equals approximately 1.9, no matter how long the sequence (Schilling, 1990). Explain why the longest number of consecutive shots made has more than a 95% chance of falling within about 4 of its mean, whether we consider 400 shots, 3200 shots, or 1 million shots.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 85CP

Chapter 6, Problem 88CP

Chapter 6 Solutions

Statistics: The Art and Science of Learning from Data (4th Edition)

Ch. 6.1 - Rolling dice a. State in a table the probability...Ch. 6.1 - Dental Insurance You plan to purchase dental...Ch. 6.1 - San Francisco Giants hitting The table shows the...Ch. 6.1 - Best of three In a best out of three series played...Ch. 6.1 - Grade distribution An instructor always assigns...Ch. 6.1 - Selling houses Let X represent the number of homes...Ch. 6.1 - Playing the lottery The state of Ohio has several...Ch. 6.1 - Roulette A roulette wheel consists of 38 numbers,...Ch. 6.1 - More Roulette The previous exercise on roulette...Ch. 6.1 - Prob. 10PB

Ch. 6.1 - Profit and the weather From past experience, a...Ch. 6.1 - Buying on eBay You are watching two items posted...Ch. 6.1 - Selling at the right price Some companies, such as...Ch. 6.1 - Uniform distribution A random number generator is...Ch. 6.1 - TV watching A social scientist uses the General...Ch. 6.2 - Probabilities in tails For a normal distribution,...Ch. 6.2 - Probability in graph For the normal distributions...Ch. 6.2 - Empirical rule Verify the empirical rule by using...Ch. 6.2 - Central probabilities For a normal distribution,...Ch. 6.2 - z-score for given probability in tails For a...Ch. 6.2 - Probability in tails for given z-score For a...Ch. 6.2 - z-score for right-tail probability a. For the...Ch. 6.2 - Prob. 23PB Ch. 6.2 - Prob. 24PB Ch. 6.2 - Prob. 25PB Ch. 6.2 - Coffee Machine Suppose your favorite coffee...Ch. 6.2 - Energy use An energy study in Gainesville,...Ch. 6.2 - Birth weight for boys In the United States, the...Ch. 6.2 - MDI The Mental Development Index (MDI) of the...Ch. 6.2 - Quartiles and outliers Refer to the previous...Ch. 6.2 - April precipitation Over roughly the past 100...Ch. 6.2 - Tall enough to ride? A new roller coaster at an...Ch. 6.2 - SAT versus ACT SAT math scores follow a normal...Ch. 6.2 - Relative height Refer to the normal distributions...Ch. 6.3 - Kidney transplants In kidney transplantations,...Ch. 6.3 - Compatible donors Refer to the previous exercise....Ch. 6.3 - Symmetric binomial Construct a graph similar to...Ch. 6.3 - Number of girls in a family Each newborn baby has...Ch. 6.3 - Prob. 39PB Ch. 6.3 - Prob. 40PB Ch. 6.3 - Passing by guessing A quiz in a statistics course...Ch. 6.3 - NBA shooting In the National Basketball...Ch. 6.3 - Season performance Refer to the previous exercise....Ch. 6.3 - Is the die balanced? A balanced die with six sides...Ch. 6.3 - Prob. 45PB Ch. 6.3 - Prob. 46PB Ch. 6.3 - Prob. 47PB Ch. 6.3 - Checking guidelines For Example 13 on the gender...Ch. 6.3 - Class sample Four of the 20 students (20%) in a...Ch. 6.3 - Prob. 50PB Ch. 6.3 - Binomial assumptions For the following random...Ch. 6 - Grandparents Let X = the number of living...Ch. 6 - Straight or boxed? Consider a Pick-3 lottery such...Ch. 6 - Auctioning paintings A collector is interested in...Ch. 6 - Prob. 55CP Ch. 6 - Are you risk averse? You need to choose between...Ch. 6 - Flyers insurance An insurance company sells a...Ch. 6 - Normal probabilities For a normal distribution,...Ch. 6 - Prob. 59CP Ch. 6 - Prob. 60CP Ch. 6 - Quartiles If z is the positive number such that...Ch. 6 - Boys and girls birth weight Exercise 6.28...Ch. 6 - Cholesterol The American Heart Association reports...Ch. 6 - Female heights Female heights in North America...Ch. 6 - Cloning butterflies The wingspans of recently...Ch. 6 - Gestation times For 5459 pregnant women using...Ch. 6 - Used car prices Data from the Web site carmax.com...Ch. 6 - Used car deals Refer to the previous exercise....Ch. 6 - Global warming Suppose that weekly use of gasoline...Ch. 6 - Fast-food profits Macs fast-food restaurant finds...Ch. 6 - Metric height A Dutch researcher reads that male...Ch. 6 - Manufacturing tennis balls According to the rules...Ch. 6 - Brides choice of surname According to a study done...Ch. 6 - Prob. 74CP Ch. 6 - Prob. 75CP Ch. 6 - Prob. 76CP Ch. 6 - Weather A weather forecaster states, The chance of...Ch. 6 - Dating success Based on past experience, Julio...Ch. 6 - Canadian lottery In one Canadian lottery option,...Ch. 6 - Likes on Facebook A large retail chain sends out...Ch. 6 - Likes with online credit The retail chain from the...Ch. 6 - Which distribution for sales? A salesperson uses...Ch. 6 - Best of five Example 2 gave the probability...Ch. 6 - Prob. 84CP Ch. 6 - Prob. 85CP Ch. 6 - Longest streak made In basketball, when the...Ch. 6 - Airline overbooking For the Boston to Chicago...Ch. 6 - Prob. 89CP Ch. 6 - Prob. 90CP Ch. 6 - Prob. 91CP Ch. 6 - Prob. 92CP Ch. 6 - Prob. 93CP Ch. 6 - Prob. 94CP Ch. 6 - Prob. 95CP Ch. 6 - Prob. 96CP Ch. 6 - Prob. 97CP Ch. 6 - Prob. 98CP Ch. 6 - Prob. 99CP Ch. 6 - Prob. 100CP Ch. 6 - Prob. 101CP

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Solution Summary: The author explains how the mean changes for each doubling of the number of shots taken and interprets it.

Concept explainers

Videos

Want to see the full answer?

Chapter 6 Solutions