Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 7.7, Problem 103E
Consider the following 10 observations on the lifetime (in hours) for a certain type of power supply: 152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, and 422.6. Construct a normal
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Results of tossing a coin four times: H, H, H, H
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Calculate the % deviation.
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Cycles to
failure
Position in
ascending
order
0.5
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(x;)
Problem 44
Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs.
To simulate real-world cake consumption, she designs a test where cakes are subjected to repeated fork stabs and bites, mimicking the brutal
reality of birthday parties. After rigorous testing, Marsha records 10 observations of how many stabs each cake endured before structural failure.
Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the
table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail.
Observation
Empirical
cumulative
Probability distribution
Cumulative distribution
Inverse of cumulative
distribution F-1 (-0.5)
F(x))
(S)
n
4
3
1
0.05
9
5
2
0.15
7
7
3
0.25
1
10
4
0.35
3
12
5
0.45
Normal…
Problem 3
In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that
their machine still struggles with power inconsistencies-sometimes generating too little energy, other times
too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far
future, they must calibrate the machine's power output. After extensive testing, they found that the time
machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a
standard deviation of 1.2 gigawatts.
The Time Travel Safety Board has set strict guidelines: For a successful time jump, the
machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly
selected time jump meets this precision requirement?
Daniel suggests that adjusting the mean power output could improve time-travel accuracy.
Can adjusting the mean reduce the number of dangerous misjumps? If yes, what should the…
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. 6ECh. 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. 38ECh. 7.4 - Prob. 39ECh. 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. 60ECh. 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. 99ECh. 7.7 - Prob. 100ECh. 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. 104ECh. 7.7 - Prob. 105ECh. 7.7 - Prob. 106ECh. 7.7 - Prob. 107ECh. 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. 113ECh. 7.8 - Prob. 114ECh. 7.8 - Prob. 115ECh. 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. 124CRCh. 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. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - Two shipping services offer overnight delivery of...Ch. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - The Cedar Rapids Gazette (November 20, 1999)...Ch. 7 - Prob. 11CRECh. 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. 16CRECh. 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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