Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
thumb_up100%
Chapter 3.5, Problem 78E
According to the article “Characterizing the Severity and Risk of Drought in the Poudre River, Colorado” (J. of Water Res. Planning and Algmnt., 2005: 383-393), the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). The cited paper proposes a geometric distribution with p = .409 for this random variable.
- a. What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?
- b. What is the probability that the length of a drought exceeds its
mean value by at least one standard deviation?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Alcohol use in the United States increased during the first year of the COVID pandemic, as did the
number of alcohol-induced deaths (such as alcoholic liver disease, accidental alcohol poisoning,
disorders due to acute intoxication).
Here is a figure from the CDC representing the "Rates of alcohol-induced deaths in the United
States in 2020, broken down by sex and age group."
Figure 2. Rates of alcohol-induced deaths, by sex and age group: United States, 2020
Age group (years)
Under 25 0.1
25-34
35-44
45-54
55-64
65-74
75-84
85 and over
Under 25
25-34
35-44
45-54
55-64
65-74
75-84
85 and over
0
0.3
3.9
2.9
6.4
10.2
7.9
10
12.9
12.8
16.7
20
21.0
21.8
24.5
Female
Male
38.5
SOURCE: National Center for Health Statistics, National Vital Statistics System, Mortality.
I
40
43.4
30
Deaths per 100,000 population
50
59.0
I
60
70
Interpret the bottom-most bar (gray bar with the value "12.8" written next to it) as a sentence in
context.
Enter your answer here
Select ALL correct interpretations of…
The attached cost-output data were obtained as part of a study of the economies of scale in operating a charter high school in Wisconsin:What type of cost-output relationship (linear, quadratic, cubic) is suggested by these statistical results?
The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds” (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s–136s) reports an experiment to predict various properties of titanium welds. Among other properties, the elongation (in %) was measured, along with the oxygen content and nitrogen content (both in percent). The following MINITAB output presents results of fitting the model
The regression equation is
Elongation = 46.80 – 130.11 Oxygen – 807.1 Nitrogen + 3580.5 Oxy*Nit
Predictor
Coef
SE Coef
T
P
Constant
46.802
3.702
12.64
0.000
Oxygen
– 130.11
20.467
– 6.36
0.000
Nitrogen
– 807.10
158.03
– 5.107
0.000
Oxy*Nit
3580.5
958.05
3.737
0.001
S = 2.809
R-Sq = 74.5%
R-Sq(adj) = 72.3%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
3
805.43
268.48
34.03
0.000
Residual Error
35
276.11
7.89
Total
38
1081.54
a. Predict the…
Chapter 3 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 3.1 - A concrete beam may fail either by shear (S) or...Ch. 3.1 - Using the experiment in Example 3.3, define two...Ch. 3.1 - Let X = the number of nonzero digits in a randomly...Ch. 3.1 - If the sample space S is an infinite set, does...Ch. 3.1 - Starting at a fixed time, each car entering an...Ch. 3.1 - For each random variable defined here, describe...Ch. 3.1 - Each time a component is tested, the trial is a...Ch. 3.1 - An individual named Claudius is located at the...Ch. 3.1 - The number of pumps in use at both a six-pump...Ch. 3.2 - Let X be the number of students who show up for a...
Ch. 3.2 - Airlines sometimes overbook flights. Suppose that...Ch. 3.2 - A mail-order computer business has six telephone...Ch. 3.2 - A contractor is required by a county planning...Ch. 3.2 - Many manufacturers have quality control programs...Ch. 3.2 - Some parts of California are particularly...Ch. 3.2 - A now batterys voltage may be acceptable (A) or...Ch. 3.2 - Two fair six-sided dice are tossed independently....Ch. 3.2 - A library subscribes to two different weekly news...Ch. 3.2 - Three couples and two single individuals have been...Ch. 3.2 - Suppose that you read through this years issues of...Ch. 3.2 - Refer to Exercise 13, and calculate and graph the...Ch. 3.2 - A branch of a certain bank in New York City has...Ch. 3.2 - An insurance company offers its policyholders a...Ch. 3.2 - In Example 3.12, let Y = the number of girls born...Ch. 3.2 - Alvie Singer lives at 0 in the accompanying...Ch. 3.2 - After all students have left the classroom, a...Ch. 3.2 - Show that the cdf F(x) is a nondecreasing...Ch. 3.3 - The pmf of the amount of memory X(GB) in a...Ch. 3.3 - An individual who has automobile insurance from a...Ch. 3.3 - Refer to Exercise 12 and calculate V(Y) and Y....Ch. 3.3 - A certain brand of upright freezer is available in...Ch. 3.3 - Let X be a Bernoulli rv with pmf as in Example...Ch. 3.3 - Suppose that the number of plants of a particular...Ch. 3.3 - A small market orders copies of a certain magazine...Ch. 3.3 - Let X be the damage incurred (in ) in a certain...Ch. 3.3 - The n candidates for a job have been ranked 1, 2,...Ch. 3.3 - Possible values of X, the number of components in...Ch. 3.3 - A chemical supply company currently has in stock...Ch. 3.3 - a. Draw a line graph of the pmf of X in Exercise...Ch. 3.3 - Use the definition in Expression (3.13) to prove...Ch. 3.3 - Suppose E(X) = 5 and E[X(X - 1)] = 27.5. What is...Ch. 3.3 - Write a general rule for E(X c) where c is a...Ch. 3.3 - A result called Chebyshevs inequality states that...Ch. 3.3 - If a X b, show that a E(X) b.Ch. 3.4 - Compute the following binomial probabilities...Ch. 3.4 - The article Should You Report That Fender-Bender?...Ch. 3.4 - NBC News reported on May 2. 2013. that 1 in 20...Ch. 3.4 - A company that produces fine crystal knows from...Ch. 3.4 - A particular telephone number is used to receive...Ch. 3.4 - Refer to the previous exercise. a. What is the...Ch. 3.4 - Suppose that 30% of all students who have to buy a...Ch. 3.4 - Exercise 30 (Section 3.3) gave the pmf of Y, the...Ch. 3.4 - A particular type of tennis racket comes in a...Ch. 3.4 - Twenty percent of all telephones of a certain type...Ch. 3.4 - The College Board reports that 2% of the 2 million...Ch. 3.4 - A certain type of flashlight requires two type-D...Ch. 3.4 - A very large batch of components has arrived at a...Ch. 3.4 - An ordinance requiring that a smoke detector be...Ch. 3.4 - A toll bridge charges 1.00 for passenger cars and...Ch. 3.4 - A student who is trying to write a paper for a...Ch. 3.4 - a. For fixed n, are there values of p(0 p 1) for...Ch. 3.4 - a. Show that b(x; n, 1 p) = b(n x; n, p). b....Ch. 3.4 - Show that E(X) = np when X is a binomial random...Ch. 3.4 - Customers at a gas station pay with a credit card...Ch. 3.4 - An airport limousine can accommodate up to four...Ch. 3.4 - Refer to Chebyshevs inequality given in Exercise...Ch. 3.5 - Eighteen individuals are scheduled to take a...Ch. 3.5 - Each of 12 refrigerators of a certain type has...Ch. 3.5 - An instructor who taught two sections of...Ch. 3.5 - A geologist has collected 10 specimens of basaltic...Ch. 3.5 - A personnel director interviewing 11 senior...Ch. 3.5 - Twenty pairs of individuals playing in a bridge...Ch. 3.5 - A second-stage smog alert has been called in a...Ch. 3.5 - The probability that a randomly selected box of a...Ch. 3.5 - A family decides to have children until it has...Ch. 3.5 - Three brothers and their wives decide to have...Ch. 3.5 - According to the article Characterizing the...Ch. 3.6 - The article Expectation Analysis of the...Ch. 3.6 - Let X be the number of material anomalies...Ch. 3.6 - Suppose that the number of drivers who travel...Ch. 3.6 - Consider writing onto a computer disk and then...Ch. 3.6 - An article in the Los Angeles Times (Dec. 3. 1993)...Ch. 3.6 - The Centers for Disease Control and Prevention...Ch. 3.6 - Suppose small aircraft arrive at a certain airport...Ch. 3.6 - Organisms are present in ballast water discharged...Ch. 3.6 - The number of requests for assistance received by...Ch. 3.6 - In proof testing of circuit boards, the...Ch. 3.6 - The article Reliability-Based Service-Life...Ch. 3.6 - Let X have a Poisson distribution with parameter ....Ch. 3.6 - Suppose that trees are distributed in a forest...Ch. 3.6 - Automobiles arrive at a vehicle equipment...Ch. 3.6 - a. In a Poisson process, what has to happen in...Ch. 3 - Consider a deck consisting of seven cards, marked...Ch. 3 - After shuffling a deck of 52 cards, a dealer deals...Ch. 3 - The negative binomial rv X was defined as the...Ch. 3 - Of all customers purchasing automatic garage-door...Ch. 3 - In some applications the distribution of a...Ch. 3 - A k-out-of-n system is one that will function if...Ch. 3 - A manufacturer of integrated circuit chips wishes...Ch. 3 - Of the people passing through an airport metal...Ch. 3 - An educational consulting firm is trying to decide...Ch. 3 - Consider a disease whose presence can be...Ch. 3 - Let p1 denote the probability that any particular...Ch. 3 - The purchaser of a power-generating unit requires...Ch. 3 - A plan for an executive travelers club has been...Ch. 3 - Forty percent of seeds from maize (modern-day com)...Ch. 3 - A trial has just resulted in a hung jury because...Ch. 3 - A reservation service employs five information...Ch. 3 - Grasshoppers arc distributed at random in a large...Ch. 3 - A newsstand has ordered five copies of a certain...Ch. 3 - Individuals A and B begin to play a sequence of...Ch. 3 - A test for the presence of a certain disease has...Ch. 3 - Prob. 114SECh. 3 - There are two Certified Public Accountants in a...Ch. 3 - The mode of a discrete random variable X with pmf...Ch. 3 - A computer disk storage device has ten concentric...Ch. 3 - If X is a hypergeometric rv, show directly from...Ch. 3 - Prob. 119SECh. 3 - Prob. 120SECh. 3 - Prob. 121SECh. 3 - Prob. 122SE
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
- The depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forward3.) M/M/2 Mean Arrival Rate: 20 customers/hour Mean Service Rate: 12 customers/hour Number of Servers: 2 Customer Waiting Cost $10/hour Assume an 8-hour day. Assume the customer waiting cost is based on time in the system. What is the daily cost of customer waiting?arrow_forward1. (Prob. 11-12, p. 438) An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp. 608–619) reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage). y 4.4 6.6 9.7 10.6 10.8 10.9 0.19 0.15 0.57 0.70 0.67 0.63 y 11.8 12.1 14.3 14.7 15.0 17.3 0.47 0.70 0.60 0.78 0.81 0.78 y 19.2 23.1 27.4 27.7 31.8 39.5 0.69 1.30 1.05 1.06 1.74 1.62 a. Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate here? b. Fit the simple linear regression model using the method of least squares. Find an estimate of o?. C. Estimate the mean chloride concentration for a watershed that has 1% roadway area. d. Find the fitted value corresponding to x = 0.47 and the associated residual.arrow_forward
- An article in the ASCE Journal of Energy Engineering [“Overview of Reservoir Release Improvements at 20 TVA Dams” (Vol. 125, April 1999, pp. 1–17)] presents data on dissolved oxygen concentrations in streams below 20 dams in the Tennessee Valley Authority system. The observations are (in milligrams per liter):arrow_forwardThe article "Lead Dissolution from Lead Smelter Slags Using Magnesium Chloride Solutions" (A. Xenidis, T. Lillis, and I. Hallikia, The AusIMM Proceedings, 1999:37-14) discusses an investigation of leaching rates of lead in solutions of magnesium chloride. The data in the following table (read from a graph) present the percentage of lead that has been extracted at various times (in minutes). Time (t) 4 8 16 30 60 120 Percent extracted (v) |1.2 1.6 2.3 2.8 3.6 4.4 a. The article suggests fitting a quadratic model y = Bo + B,t + Bz² + ɛ to these data. Fit this model, and compute the standard deviations of the coefficients. b. The reaction rate at time t is given by the derivative dy/dt = B, + 2B,t. Estimate the time at which the reaction rate will be equal to 0.05. c. The reaction rate at t = Oisequal to B1. Find a 95% confidence interval for the reaction rate at t = 0. d. Can you conclude that the reaction rate is decreasing with time? Explain.arrow_forwardThe article "Characteristics and Trends of River Discharge into Hudson, James, and Ungava Bays, 1964-2000" (S. Dery, M. Stieglitz, et al., Journal of Climate, 2005:2540-2557) presents measurements of discharge rate x (in kmlyr) andpeakflow y (in m/s) for 42 rivers that drain into the Hudson, James, and Ungava Bays. The data are shown in the following table: Discharge Peak Flow 94.24 4110.3 66.57 4961.7 59.79 10275.5 48.52 6616.9 40.00 7459.5 32.30 2784.4 31.20 3266.7 30.69 4368.7 26.65 1328.5 22.75 4437.6 21.20 1983.0 20.57 1320.1 19.77 1735.7 18.62 1944.1 17.96 3420.2 17.84 2655.3 16.06 3470.3 1561.6 14.69 11.63 869.8 11.19 936.8 11.08 1315.7 10.92 1727.1 9.94 768.1 7.86 483.3arrow_forward
- The following table shows the typical depth (rounded to the nearest foot) for nonfailed wells in geological formations in Baltimore County (The Journal of Data Science, 2009, Vol. 7, pp. 111-127). Geological Formation Group Number of Nonfailed Wells Nonfailed Well Depth Gneiss 1,515 255 Granite 26 218 Loch Raven Schist 3,290 317 Mafic 349 231 Marble 280 267 Prettyboy Schist 1,343 255 Other schists 887 267 Serpentine 36 217 Total 7,726 2,027 Let the random variable X denote the depth (rounded to the nearest foot) for nonfailed wells. Detemine the cumulative distribution function for X. Round your answers to four decimal places (e.g. 98.7654). x < 217 217arrow_forwardThe toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 33 33 34 31 37 46 54 49 41 50 44 56 55 61 64 59 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal…arrow_forwardThe toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 33 33 33 31 37 44 56 52 45 54 46 55 59 59 61 63 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two…arrow_forwardThe toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 34 32 33 29 38 46 58 50 46 53 44 51 57 58 59 58 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two…arrow_forwardHealth care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 47 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.7 and s = 12.1. Complete parts (a)-(d). a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy. 19.7 b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy. (16.24, 23.16) (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) c. Give a practical interpretation of the interval, part (b). OA. One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with latex allergy is greater than the…arrow_forwardQ1 An engineering student wants to study the impact of temperature and humidity on yield. The following data was recorded by the student. S.N Temperature Humidity Yield 1 40 57 112 2 45 54 118 3 50 54 128 4 55 60 121 60 66 126 65 59 136 7 70 61 144 8 75 58 142 80 59 149 10 85 56 165arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License