Introduction To Statistics And Data Analysis

6th Edition

ISBN: 9781337793612

Author: PECK, Roxy.

Publisher: Cengage Learning,

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Textbook Question

Chapter 7.2, Problem 19E

Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of the components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested until a defect-free component is obtained.

a. What is the smallest possible y value, and what outcome corresponds to this y value? What is the second smallest y value, and what is the corresponding outcome?
b. What is the set of all possible y values?
c. Calculate the probability of each of the five smallest y values. (You should see a pattern that leads to a simple formula for p(y), the probability distribution of y.)

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Chapter 7 Solutions

Introduction To Statistics And Data Analysis

Ch. 7.1 - State whether each of the following random...Ch. 7.1 - Classify each of the following random variables as...Ch. 7.1 - Starting at a particular time, each car entering...Ch. 7.1 - A point is randomly selected from the interior of...Ch. 7.1 - A point is randomly selected on the surface of a...Ch. 7.1 - Prob. 6E Ch. 7.1 - A box contains four slips of paper marked 1, 2, 3,...Ch. 7.2 - Define the random variable x to be the number of...Ch. 7.2 - Using the probability distribution given in the...Ch. 7.2 - Let y denote the number of broken eggs in a...

Ch. 7.2 - Use the probability distribution given in the...Ch. 7.2 - Suppose that fund-raisers at a university call...Ch. 7.2 - Airlines sometimes overbook flights. Suppose that...Ch. 7.2 - Suppose that a computer manufacturer receives...Ch. 7.2 - Simulate the chance experiment described in the...Ch. 7.2 - Of all airline flight requests received by a...Ch. 7.2 - Suppose that 20% of all homeowners in an...Ch. 7.2 - A box contains five slips of paper, marked 1, 1,...Ch. 7.2 - Components coming off an assembly line are either...Ch. 7.2 - When applying for a building permit, a contractor...Ch. 7.2 - A library subscribes to two different weekly news...Ch. 7.3 - Let x denote the lifetime (in thousands of hours)...Ch. 7.3 - Using the density curve for fan lifetime given in...Ch. 7.3 - A particular professor never dismisses class...Ch. 7.3 - Refer to the probability distribution given in the...Ch. 7.3 - The article Probabilistic Risk Assessment of...Ch. 7.3 - Use the density curve of x = distance of actual...Ch. 7.3 - Let x denote the amount of gravel sold (in tons)...Ch. 7.3 - Use the density curve for x = amount of gravel...Ch. 7.3 - Let x be the amount of time (in minutes) that a...Ch. 7.3 - Ref erring to the previous exercise, let x and y...Ch. 7.3 - The density curve for the random variable w (the...Ch. 7.4 - Consider selecting a household in rural Thailand...Ch. 7.4 - Suppose the probability distribution of x, the...Ch. 7.4 - Consider the following probability distribution...Ch. 7.4 - Referring to the previous exercise, use the result...Ch. 7.4 - Exercise 7.8 gave the following probability...Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Refer to the information given in Exercise 7.39....Ch. 7.4 - Refer to the information given in Exercise 7.39....Ch. 7.4 - Suppose that for a particular computer...Ch. 7.4 - A local television station sells 15-second,...Ch. 7.4 - An author has written a book and submitted it to a...Ch. 7.4 - A grocery store has an express line for customers...Ch. 7.4 - An appliance dealer sells three different models...Ch. 7.4 - To assemble a piece of furniture, a wood peg must...Ch. 7.4 - A multiple-choice exam consists of 50 questions....Ch. 7.4 - Consider a game in which a red die and a blue die...Ch. 7.4 - Consider the random variables xR and xB defined in...Ch. 7.5 - CBS News reported that 4% of adult Americans have...Ch. 7.5 - Flight View surveyed 2600 North American airline...Ch. 7.5 - Refer to the previous exercise, and suppose that...Ch. 7.5 - Twenty-five percent of the customers of a grocery...Ch. 7.5 - Example 7.18 described a study in which a person...Ch. 7.5 - Information Security Buzz provides news for the...Ch. 7.5 - A breeder of show dogs is interested in the number...Ch. 7.5 - Womens Health Magazine surveyed 1187 readers to...Ch. 7.5 - Prob. 60E Ch. 7.5 - Suppose that the probability is 0.1 that any given...Ch. 7.5 - Suppose that 30% of all automobiles undergoing an...Ch. 7.5 - Suppose that you will take a multiple-choice exam...Ch. 7.5 - Suppose that 20% of the 10,000 signatures on a...Ch. 7.5 - A city requires that smoke detectors be installed...Ch. 7.5 - Suppose that 90% of all registered California...Ch. 7.5 - Suppose a playlist on a music player consists of...Ch. 7.5 - Sophie is a dog that loves to play catch....Ch. 7.5 - Suppose that 5% of cereal boxes contain a prize...Ch. 7.6 - Determine the following standard normal (z) curve...Ch. 7.6 - Determine the following standard normal (z) curve...Ch. 7.6 - Determine each of the following areas under the...Ch. 7.6 - Determine each of the following areas under the...Ch. 7.6 - Let z denote a random variable that has a standard...Ch. 7.6 - Let z denote a random variable that has a standard...Ch. 7.6 - Let z denote a random variable having a normal...Ch. 7.6 - Let z denote a random variable having a normal...Ch. 7.6 - Let z denote a variable that has a standard normal...Ch. 7.6 - Determine the value z that a. Separates the...Ch. 7.6 - Determine the value of z such that a. z and z...Ch. 7.6 - Because P(z 0.44) = 0.67, 67% of all z values are...Ch. 7.6 - Consider the population of all 1-gallon cans of...Ch. 7.6 - Consider babies born in the normal range of 3743...Ch. 7.6 - Use the information on birth weights for babies...Ch. 7.6 - Emissions of nitrogen oxides, which are major...Ch. 7.6 - The paper referenced in Example 7.30 (Estimating...Ch. 7.6 - The size of the left upper chamber of the heart is...Ch. 7.6 - The paper referenced in the previous exercise also...Ch. 7.6 - The article New York Citys Graffiti-Removal...Ch. 7.6 - A machine that cuts corks for wine bottles...Ch. 7.6 - Refer to the previous exercise. Suppose that there...Ch. 7.6 - Purchases made at small corner stores were studied...Ch. 7.6 - The time that it takes a randomly selected job...Ch. 7.6 - Suppose that the distribution of typing speed in...Ch. 7.6 - Consider the typing speed distribution described...Ch. 7.6 - Consider the typing speed distribution described...Ch. 7.7 - The authors of the paper Development of...Ch. 7.7 - The paper Risk Behavior, Decision Making, and...Ch. 7.7 - Prob. 99E Ch. 7.7 - Prob. 100E Ch. 7.7 - Macular degeneration is the most common cause of...Ch. 7.7 - The following normal probability plot was...Ch. 7.7 - Consider the following 10 observations on the...Ch. 7.7 - Prob. 104E Ch. 7.7 - Prob. 105E Ch. 7.7 - Prob. 106E Ch. 7.7 - Prob. 107E Ch. 7.7 - The figure on the next page appeared in the paper...Ch. 7.8 - Let x denote the IQ of an individual selected at...Ch. 7.8 - Suppose that the distribution of x = the number of...Ch. 7.8 - The number of vehicles leaving a turnpike at a...Ch. 7.8 - Suppose that x has a binomial distribution with n...Ch. 7.8 - Prob. 113E Ch. 7.8 - Prob. 114E Ch. 7.8 - Prob. 115E Ch. 7.8 - Suppose that 70% of the bicycles sold by a certain...Ch. 7.8 - Suppose that 25% of the fire alarms in a large...Ch. 7.8 - Suppose that 65% of all registered voters in a...Ch. 7.8 - Flashlight bulbs manufactured by a certain company...Ch. 7.8 - A company that manufactures mufflers for cars...Ch. 7 - Let x denote the duration of a randomly selected...Ch. 7 - A soft-drink machine dispenses only regular Coke...Ch. 7 - A business has six customer service telephone...Ch. 7 - Prob. 124CR Ch. 7 - Refer 10 the probability distribution given in...Ch. 7 - A new batterys voltage may be acceptable (A) or...Ch. 7 - A pizza company advertises that it puts 0.5 pounds...Ch. 7 - Suppose that fuel efficiency for a particular...Ch. 7 - A coin is flipped 25 times. Let x be the number of...Ch. 7 - The probability distribution of x, the number of...Ch. 7 - The amount of time spent by a statistical...Ch. 7 - The lifetime of a certain brand of battery is...Ch. 7 - A machine producing vitamin E capsules operates so...Ch. 7 - The Wall Street Journal (February 15, 1972)...Ch. 7 - The longest run of Ss in the sequence SSFSSSSFFS...Ch. 7 - Four peoplea, b, c, and dare waiting to give...Ch. 7 - Kyle and Lygia are going to play a series of...Ch. 7 - Suppose that your statistics professor tells you...Ch. 7 - Suppose that the pH of soil samples taken from a...Ch. 7 - The lightbulbs used to provide exterior lighting...Ch. 7 - Suppose there are approximately 40,000 travel...Ch. 7 - Prob. 2CRE Ch. 7 - Prob. 3CRE Ch. 7 - Prob. 5CRE Ch. 7 - Prob. 6CRE Ch. 7 - Two shipping services offer overnight delivery of...Ch. 7 - Prob. 8CRE Ch. 7 - Prob. 9CRE Ch. 7 - The Cedar Rapids Gazette (November 20, 1999)...Ch. 7 - Prob. 11CRE Ch. 7 - The article Men, Women at Odds on Gun Control...Ch. 7 - Suppose that a new Internet company Mumble.com...Ch. 7 - Refer to the previous exercise. Suppose that...Ch. 7 - A chemical supply company currently has in stock...Ch. 7 - Prob. 16CRE Ch. 7 - An experiment was conducted to investigate whether...Ch. 7 - A machine that produces ball bearings has...Ch. 7 - Consider the variable x = time required for a...Ch. 7 - The accompanying data on x = student-teacher ratio...Ch. 7 - Prob. 21CRE

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Solution Summary: The author explains that the random variable y is defined as the number of components that are tested until a defect-free component is obtained.

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Chapter 7 Solutions