Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6.3, Problem 6.33E
Under what circumstances should the hypergeometric distribution be used instead o the binomial distribution?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Cycles to
failure
Position in
ascending
order
0.5
f(x))
(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…
Problem 5 (
Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain
America's shield), so she decides to start a detailed literature review on the subject. Among others, she found
a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing
mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is
shown in the table below.
a.
Run
A
B
с
D
1
(1)
-1
-1
-1
1
2
a
1
-1
-1
1
3
bd
-1
1
-1
1
4
abd
1
1
-1
1
5
cd
-1
-1
1
-1
6
acd
1
-1
1
-1
7
bc
-1
1
1
-1
abc
1
1
1
-1
paper?
s) What was the generator used in the 2"(4-1) fractional factorial design described in the
b.
Based on the resolution of this design, what do you think about the generator used in the
paper? Do you think it was a good choice, or would you have selected a different one? Explain your
answer in detail.
Chapter 6 Solutions
Introduction to Business Statistics
Ch. 6.1 - Prob. 6.1ECh. 6.1 - Indicate whether each of the following random...Ch. 6.1 - Indicate whether each of the following random...Ch. 6.1 - Prob. 6.4ECh. 6.1 - Prob. 6.5ECh. 6.1 - Determine the mean, variance, and standard...Ch. 6.1 - Determine the mean, variance, and standard...Ch. 6.1 - Prob. 6.8ECh. 6.1 - Prob. 6.9ECh. 6.1 - Prob. 6.10E
Ch. 6.1 - A consultant has presented his client with three...Ch. 6.1 - Prob. 6.12ECh. 6.1 - Prob. 6.13ECh. 6.1 - Laura McCarthy, the owner of Riverside Bakery, has...Ch. 6.1 - In 2007, nearly 24 million tons of steel mill...Ch. 6.2 - What is necessary for a process to be considered a...Ch. 6.2 - When we are sampling without replacement, under...Ch. 6.2 - Prob. 6.18ECh. 6.2 - Prob. 6.19ECh. 6.2 - A city law-enforcement official has stated that...Ch. 6.2 - Prob. 6.21ECh. 6.2 - According to the National Marine Manufacturers...Ch. 6.2 - In the town of Hickoryville, an adult citizen has...Ch. 6.2 - It has been reported that the overall graduation...Ch. 6.2 - Prob. 6.25ECh. 6.2 - The U.S. Department of Labor has reported that 30%...Ch. 6.2 - Alicia’s schedule includes three Tuesday/Thursday...Ch. 6.2 - OfficeQuip is a small office supply firm that is...Ch. 6.2 - Four wheel bearings are to be replaced on a...Ch. 6.2 - It has been estimated that one in five Americans...Ch. 6.2 - Airlines book more seats than arc actually...Ch. 6.2 - Every day, artists at Arnold’s House of Fine...Ch. 6.3 - Under what circumstances should the hypergeometric...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - Using the hypergeometric distribution, with...Ch. 6.3 - In a criminal trial, there are 25 persons who have...Ch. 6.3 - A computer firm must send a group of three...Ch. 6.3 - Prob. 6.38ECh. 6.4 - Prob. 6.39ECh. 6.4 - Prob. 6.40ECh. 6.4 - Prob. 6.41ECh. 6.4 - Prob. 6.42ECh. 6.4 - The U.S. divorce rate has been reported as 3.6...Ch. 6.4 - During the 12 P.M.-1 P.M. noon hour, arrivals at a...Ch. 6.4 - During the winter heating season in a northern...Ch. 6.4 - Prob. 6.46ECh. 6.4 - Prob. 6.47ECh. 6.4 - Prob. 6.48ECh. 6.4 - Prob. 6.49ECh. 6.4 - A manufacturing plant’s main production line...Ch. 6.4 - Prob. 6.51ECh. 6 - The owner of a charter fishing boat has found that...Ch. 6 - Prob. 6.55CECh. 6 - Prob. 6.56CECh. 6 - Prob. 6.57CECh. 6 - Prob. 6.58CECh. 6 - Prob. 6.59CECh. 6 - Prob. 6.60CECh. 6 - A mining company finds that daily lost-work...Ch. 6 - Prob. 6.62CECh. 6 - Prob. 6.63CECh. 6 - Prob. 6.64CECh. 6 - Prob. 6.65CECh. 6 - Seven of the 15 campus police officers available...Ch. 6 - Prob. 6.67CECh. 6 - Prob. 6.68CECh. 6 - Prob. 6.69CECh. 6 - Prob. 6.70CECh. 6 - Prob. 6.71CECh. 6 - Prob. 6.72CECh. 6 - Prob. 6.73CECh. 6 - Prob. 6.74CECh. 6 - Prob. 6.75CECh. 6 - Prob. 6.76CECh. 6 - Prob. 6.77CECh. 6 - Prob. 6.78CECh. 6 - Prob. 6.79CECh. 6 - Prob. 6.80CE
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
- Suppose we wish to test the hypothesis that women with a sister’s history of breast cancer are at higher risk of developing breast cancer themselves. Suppose we assume that the prevalence rate of breast cancer is 3% among 60- to 64-year-old U.S. women, whereas it is 5% among women with a sister history. We propose to interview 400 women 40 to 64 years of age with a sister history of the disease. What is the power of such a study assuming that the level of significance is 10%? I only need help writing the null and alternative hypotheses.arrow_forward4.96 The breaking strengths for 1-foot-square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,250 pounds per square inch (psi) and a standard deviation of 10.2 psi. Find the probability of selecting a 1-foot-square sample of material at random that on testing would have a breaking strength in excess of 2,265 psi.4.97 Refer to Exercise 4.96. Suppose that a new synthetic fabric has been developed that may have a different mean breaking strength. A random sample of 15 1-foot sections is obtained, and each section is tested for breaking strength. If we assume that the population standard deviation for the new fabric is identical to that for the old fabric, describe the sampling distribution forybased on random samples of 15 1-foot sections of new fabricarrow_forwardUne Entreprise œuvrant dans le domaine du multividéo donne l'opportunité à ses programmeurs-analystes d'évaluer la performance des cadres supérieurs. Voici les résultats obtenues (sur une échelle de 10 à 50) où 50 représentent une excellente performance. 10 programmeurs furent sélectionnés au hazard pour évaluer deux cadres. Un rapport Excel est également fourni. Programmeurs Cadre A Cadre B 1 34 36 2 32 34 3 18 19 33 38 19 21 21 23 7 35 34 8 20 20 9 34 34 10 36 34 Test d'égalité des espérances: observations pairéesarrow_forward
- A television news channel samples 25 gas stations from its local area and uses the results to estimate the average gas price for the state. What’s wrong with its margin of error?arrow_forwardYou’re fed up with keeping Fido locked inside, so you conduct a mail survey to find out people’s opinions on the new dog barking ordinance in a certain city. Of the 10,000 people who receive surveys, 1,000 respond, and only 80 are in favor of it. You calculate the margin of error to be 1.2 percent. Explain why this reported margin of error is misleading.arrow_forwardYou find out that the dietary scale you use each day is off by a factor of 2 ounces (over — at least that’s what you say!). The margin of error for your scale was plus or minus 0.5 ounces before you found this out. What’s the margin of error now?arrow_forward
- Suppose that Sue and Bill each make a confidence interval out of the same data set, but Sue wants a confidence level of 80 percent compared to Bill’s 90 percent. How do their margins of error compare?arrow_forwardSuppose that you conduct a study twice, and the second time you use four times as many people as you did the first time. How does the change affect your margin of error? (Assume the other components remain constant.)arrow_forwardOut of a sample of 200 babysitters, 70 percent are girls, and 30 percent are guys. What’s the margin of error for the percentage of female babysitters? Assume 95 percent confidence.What’s the margin of error for the percentage of male babysitters? Assume 95 percent confidence.arrow_forward
- You sample 100 fish in Pond A at the fish hatchery and find that they average 5.5 inches with a standard deviation of 1 inch. Your sample of 100 fish from Pond B has the same mean, but the standard deviation is 2 inches. How do the margins of error compare? (Assume the confidence levels are the same.)arrow_forwardA survey of 1,000 dental patients produces 450 people who floss their teeth adequately. What’s the margin of error for this result? Assume 90 percent confidence.arrow_forwardThe annual aggregate claim amount of an insurer follows a compound Poisson distribution with parameter 1,000. Individual claim amounts follow a Gamma distribution with shape parameter a = 750 and rate parameter λ = 0.25. 1. Generate 20,000 simulated aggregate claim values for the insurer, using a random number generator seed of 955.Display the first five simulated claim values in your answer script using the R function head(). 2. Plot the empirical density function of the simulated aggregate claim values from Question 1, setting the x-axis range from 2,600,000 to 3,300,000 and the y-axis range from 0 to 0.0000045. 3. Suggest a suitable distribution, including its parameters, that approximates the simulated aggregate claim values from Question 1. 4. Generate 20,000 values from your suggested distribution in Question 3 using a random number generator seed of 955. Use the R function head() to display the first five generated values in your answer script. 5. Plot the empirical density…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License