Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5.2, Problem 1AC
Radiation Exposure
On March 28, 1979, the nuclear generating facility at Three Mile Island, Pennsylvania, began discharging radiation into the atmosphere. People exposed to even low levels of radiation can experience health problems
1. What does expected value
2. Would you expect the exact value of 3 all the time?
3. If a news reporter stated that the number of cases of kidney problems in newborns was nearly four times as many as was usually expected, do you think pregnant mothers living in that area would be overly concerned?
4. Is it unlikely that 11 occurred by chance?
5. Are there any other statistics that could better inform the public?
6. Assume that 3 out of 2500 babies were born with kidney problems in that three-county area the year before the accident. Also assume that 11 out of 2500 babies were born with kidney problems in that three-county area the year after the accident. What is the real percentage increase in that abnormality?
7. Do you think that pregnant mothers living in that area should be overly concerned after looking at the results in terms of rates?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 5 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 5.1 - Dropping College Courses Use the following table...Ch. 5.1 - Define and give three examples of a random...Ch. 5.1 - Explain the difference between a discrete and a...Ch. 5.1 - Give three examples of a discrete random variable.Ch. 5.1 - Give three examples of a continuous random...Ch. 5.1 - List three continuous random variables and three...Ch. 5.1 - What is a probability distribution? Give an...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...
Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 7 through 12, determine whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 13 through 18, state whether the...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - For Exercises 19 through 26, construct a...Ch. 5.1 - Triangular Numbers The first six triangular...Ch. 5.1 - Child Play in Day Care In a popular day care...Ch. 5.1 - Goals in Hockey The probability that a hockey team...Ch. 5.1 - Mathematics Tutoring Center At a drop-in...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - For Exercises 31 through 36, write the...Ch. 5.1 - Computer Games The probability that a child plays...Ch. 5.2 - Radiation Exposure On March 28, 1979, the nuclear...Ch. 5.2 - Coffee with Meals A researcher wishes to determine...Ch. 5.2 - Suit Sales The number of suits sold per day at a...Ch. 5.2 - Daily Newspapers A survey was taken of the number...Ch. 5.2 - Trivia Quiz The probabilities that a player will...Ch. 5.2 - New Homes A contractor has four new home plans....Ch. 5.2 - Traffic Accidents The county highway department...Ch. 5.2 - Fitness Machine A fitness center bought a new...Ch. 5.2 - Benfords Law The leading digits in actual data,...Ch. 5.2 - Automobiles A survey shows the probability of the...Ch. 5.2 - Pizza Deliveries A pizza shop owner determines the...Ch. 5.2 - Grab Bags A convenience store has made up 20 grab...Ch. 5.2 - Job Bids A landscape contractor bids on jobs where...Ch. 5.2 - Rolling Dice If a person rolls doubles when she...Ch. 5.2 - Dice Game A person pays 2 to play a certain game...Ch. 5.2 - Lottery Prizes A lottery offers one 1000 prize,...Ch. 5.2 - Winning the Lottery For a daily lottery, a person...Ch. 5.2 - Life Insurance A 35-year-old woman purchases a...Ch. 5.2 - Roulette A roulette wheel has 38 numbers, 1...Ch. 5.2 - Rolling Dice Construct a probability distribution...Ch. 5.2 - Rolling a Die When one die is rolled, the expected...Ch. 5.2 - The formula for finding the variance for a...Ch. 5.2 - Complete the following probability distribution if...Ch. 5.2 - Probability Distribution A bag contains five balls...Ch. 5.3 - Unsanitary Restaurants Health officials routinely...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Which of the following are binomial experiments or...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Compute the probability of X successes, using the...Ch. 5.3 - Belief in UFOs A survey found that 10% of...Ch. 5.3 - Multiple-Choice Exam A student takes a...Ch. 5.3 - High Blood Pressure Twenty percent of Americans...Ch. 5.3 - High School Dropouts Approximately 10.3% of...Ch. 5.3 - Advertising Three out of four people think most...Ch. 5.3 - Language Spoken at Home by the U.S. Population In...Ch. 5.3 - Prison Inmates Forty percent of prison inmates...Ch. 5.3 - Destination Weddings Twenty-six percent of couples...Ch. 5.3 - People Who Have Some College Education Fifty-three...Ch. 5.3 - Guidance Missile System A missile guidance system...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Find the mean, variance, and standard deviation...Ch. 5.3 - Airline Accidents Twenty-five percent of...Ch. 5.3 - Tossing Coins Find the mean, variance, and...Ch. 5.3 - American and Foreign-Born Citizens In 2014 the...Ch. 5.3 - Federal Government Employee E-mail Use It has been...Ch. 5.3 - Watching Fireworks A survey found that 21% of...Ch. 5.3 - Alternate Sources of Fuel Eighty-five percent of...Ch. 5.3 - Survey on Bathing Pets A survey found that 25% of...Ch. 5.3 - Survey on Answering Machine Ownership In a survey,...Ch. 5.3 - Poverty and the Federal Government One out of...Ch. 5.3 - Internet Purchases Thirty-two percent of adult...Ch. 5.3 - Prob. 29ECh. 5.3 - Job Elimination In a recent year, 13% of...Ch. 5.3 - Survey of High School Seniors Of graduating high...Ch. 5.3 - Is this a binomial distribution? Explain.Ch. 5.3 - Children in a Family The graph shown here...Ch. 5.3 - Construct a binomial distribution graph for the...Ch. 5.3 - Show that the mean for a binomial random variable...Ch. 5.4 - Rockets and Targets During the latter days of...Ch. 5.4 - Use the multinomial formula and find the...Ch. 5.4 - Use the multinomial formula and find the...Ch. 5.4 - MMs Color Distribution According to the...Ch. 5.4 - Truck Inspection Violations The probabilities are...Ch. 5.4 - Prob. 5ECh. 5.4 - Mendels Theory According to Mendels theory, if...Ch. 5.4 - Find each probability P(X; ), using Table C in...Ch. 5.4 - Find each probability P(X; ) using Table C in...Ch. 5.4 - Study of Robberies A recent study of robberies for...Ch. 5.4 - Misprints on Manuscript Pages In a 400-page...Ch. 5.4 - Colors of Flowers A nursery provides red impatiens...Ch. 5.4 - Mail Ordering A mail-order company receives an...Ch. 5.4 - Company Mailing Of a companys mailings 1.5% are...Ch. 5.4 - Emission Inspection Failures If 3% of all cars...Ch. 5.4 - Phone Inquiries The average number of phone...Ch. 5.4 - Defective Calculators In a batch of 2000...Ch. 5.4 - School Newspaper Staff A school newspaper staff is...Ch. 5.4 - Job Applicants Twelve people apply for a teaching...Ch. 5.4 - Prob. 19ECh. 5.4 - Defective Computer Keyboards A shipment of 24...Ch. 5.4 - Defective Electronics A shipment of 24 smartphones...Ch. 5.4 - Job Applications Ten people apply for a job at...Ch. 5.4 - Auto Repair Insurance A person calls people to ask...Ch. 5.4 - Prob. 24ECh. 5.4 - Shooting an Arrow Mark shoots arrows at a target...Ch. 5.4 - Amusement Park Game At an amusement park...Ch. 5.4 - Prob. 27ECCh. 5.4 - Prob. 28ECCh. 5.4 - Drawing Cards Cards are drawn at random from a...Ch. 5.4 - Prob. 30ECCh. 5.4 - Prob. 31ECCh. 5.4 - Lessons Outside of School About 2 out of every 3...Ch. 5.4 - Prob. 33ECCh. 5.4 - Work versus Conscience One worker in four in...Ch. 5 - For Exercises 1 through 3, determine whether the...Ch. 5 - For Exercises 1 through 3, determine whether the...Ch. 5 - Prob. 5.1.3RECh. 5 - Prob. 5.1.4RECh. 5 - Credit Cards A large retail company encourages its...Ch. 5 - Prob. 5.1.6RECh. 5 - Shoe Purchases At Shoe World, the manager finds...Ch. 5 - Prob. 5.2.8RECh. 5 - Arrivals at an Airport At a small rural airport,...Ch. 5 - Cans of Paint Purchased During a recent paint sale...Ch. 5 - Phone Customers A phone service center keeps track...Ch. 5 - Outdoor Regatta A producer plans an outdoor...Ch. 5 - Card Game A game is set up as follows: All the...Ch. 5 - Card Game Using Exercise 13, how much should be...Ch. 5 - Let x be a binomial random variable with n = 12...Ch. 5 - Internet Access via Cell Phone In a retirement...Ch. 5 - Self-Driving Automobile Fifty-eight percent of...Ch. 5 - Prob. 5.3.18RECh. 5 - U.S. Police Chiefs and the Death Penalty The...Ch. 5 - Prob. 5.3.20RECh. 5 - Pizza for Breakfast Three out of four American...Ch. 5 - Prob. 5.3.22RECh. 5 - Prob. 5.4.23RECh. 5 - Prob. 5.4.24RECh. 5 - Accounting Errors The probability that an...Ch. 5 - Prob. 5.4.26RECh. 5 - Prob. 5.4.27RECh. 5 - Boating Accidents The number of boating accidents...Ch. 5 - Prob. 5.4.29RECh. 5 - Prob. 5.4.30RECh. 5 - Items Donated to a Food Bank At a food bank a case...Ch. 5 - Prob. 5.4.32RECh. 5 - Prob. 5.4.33RECh. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Determine whether each statement is true or false....Ch. 5 - Complete these statements with the best answer. 5....Ch. 5 - Complete these statements with the best answer. 6....Ch. 5 - Complete these statements with the best answer. 7....Ch. 5 - Select the best answer. 8. What is the sum of the...Ch. 5 - Select the best answer. 9. How many outcomes are...Ch. 5 - Select the best answer. 10. The number of trials...Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - For exercises 11 through 14, determine if the...Ch. 5 - For exercises 11 through 14, determine if the...Ch. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Calls for a Crisis Hot Line The number of calls...Ch. 5 - Selecting a Card There are 6 playing cards placed...Ch. 5 - Prob. 20CQCh. 5 - Carpooling If 40% of all commuters ride to work in...Ch. 5 - Employed Women If 60% of all women are employed...Ch. 5 - Prob. 23CQCh. 5 - Meeting Attendance A history class has 75 members....Ch. 5 - Prob. 25CQCh. 5 - Quality Control Check Before a television set...Ch. 5 - Bowling Team Uniforms Among the teams in a bowling...Ch. 5 - Elm Trees If 8% of the population of trees are elm...Ch. 5 - Sports Score Hot Line Calls Sports Scores Hot Line...Ch. 5 - Color of Raincoats There are 48 raincoats for sale...Ch. 5 - Youth Group Officers A youth group has 8 boys and...Ch. 5 - Blood Types About 4% of the citizens of the United...Ch. 5 - Alcohol Abstainers About 35% of Americans abstain...Ch. 5 - Prob. 1CTCCh. 5 - Prob. 2CTCCh. 5 - Prob. 3CTCCh. 5 - Prob. 4CTCCh. 5 - Prob. 5CTC
Knowledge Booster
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.Similar questions
- 2. Hypothesis Testing - Two Sample Means A nutritionist is investigating the effect of two different diet programs, A and B, on weight loss. Two independent samples of adults were randomly assigned to each diet for 12 weeks. The weight losses (in kg) are normally distributed. Sample A: n = 35, 4.8, s = 1.2 Sample B: n=40, 4.3, 8 = 1.0 Questions: a) State the null and alternative hypotheses to test whether there is a significant difference in mean weight loss between the two diet programs. b) Perform a hypothesis test at the 5% significance level and interpret the result. c) Compute a 95% confidence interval for the difference in means and interpret it. d) Discuss assumptions of this test and explain how violations of these assumptions could impact the results.arrow_forward1. Sampling Distribution and the Central Limit Theorem A company produces batteries with a mean lifetime of 300 hours and a standard deviation of 50 hours. The lifetimes are not normally distributed—they are right-skewed due to some batteries lasting unusually long. Suppose a quality control analyst selects a random sample of 64 batteries from a large production batch. Questions: a) Explain whether the distribution of sample means will be approximately normal. Justify your answer using the Central Limit Theorem. b) Compute the mean and standard deviation of the sampling distribution of the sample mean. c) What is the probability that the sample mean lifetime of the 64 batteries exceeds 310 hours? d) Discuss how the sample size affects the shape and variability of the sampling distribution.arrow_forwardA biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?arrow_forward
- Businessarrow_forwardWhat is the solution and answer to question?arrow_forwardTo: [Boss's Name] From: Nathaniel D Sain Date: 4/5/2025 Subject: Decision Analysis for Business Scenario Introduction to the Business Scenario Our delivery services business has been experiencing steady growth, leading to an increased demand for faster and more efficient deliveries. To meet this demand, we must decide on the best strategy to expand our fleet. The three possible alternatives under consideration are purchasing new delivery vehicles, leasing vehicles, or partnering with third-party drivers. The decision must account for various external factors, including fuel price fluctuations, demand stability, and competition growth, which we categorize as the states of nature. Each alternative presents unique advantages and challenges, and our goal is to select the most viable option using a structured decision-making approach. Alternatives and States of Nature The three alternatives for fleet expansion were chosen based on their cost implications, operational efficiency, and…arrow_forward
- The following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8arrow_forwardII Consider the following data matrix X: X1 X2 0.5 0.4 0.2 0.5 0.5 0.5 10.3 10 10.1 10.4 10.1 10.5 What will the resulting clusters be when using the k-Means method with k = 2. In your own words, explain why this result is indeed expected, i.e. why this clustering minimises the ESS map.arrow_forwardwhy the answer is 3 and 10?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License