Concept explainers
The article “Microwave Observations of Daily Antarctic Sea-Ice Edge Expansion and Contribution Rates” (IEEE Geosci. and Remote Sensing Letters, 2006: 54–58) states that “The distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential.” The proposed double exponential distribution has density
a. What is the value of the parameter λ?
b. What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the
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Probability and Statistics for Engineering and the Sciences
- A prospective cohort study is run to estimate the incidence of stroke in persons 55 years of age and older. All participants are free of stroke at study start. Each participant is followed for a maximum of 5 years. The data are summarized in Table 3–14. Number of Strokes Number of Stroke-Free Person-Years Men (n = 125) 9 478 Women (n = 200) 21 97 What is the annual incidence rate of stroke in men? What is the annual incidence rate of stroke in women? What is the annual incidence rate of stroke (men and women combined)?arrow_forwardCONSTRUCT MODIFIED BOXPLOT To understand better the effects of exercise and aging on various cireulatory functions, the article "Cardiac Output in Male Middle-Aged Runners" (Journal of Sports Medicine [1982]: 17–22) presented data from a study of 21 middle-aged male runners. The following data set gives values of oxygen capacity values (in milliliters per kilo- gram per minute) while the participants pedaled at a speci- fied rate on a bicycle ergometer: 12.81 14.95 15.83 15.97 17.90 18.27 18.34 19.82 19.94 20.62 20.88 20.93 20.98 20.99 21.15 22.16 22.24 23.16 23.56 35.78 36.73 a. Compute the median and the quartiles for this data set. b. What is the value of the interquartile range? Are there outliers in this data set? c. Draw a modified boxplot, and comment on the interest- ing features of the plot.arrow_forwardA study was performed looking at the risk of fractures in three rural Iowa communities according to whether their drinking water was “higher calcium,” “higher fluorides,” or “control” as determined by water samples. Table 11.10 presents data comparing the rate of fractures (over 5 years) between the higher-calcium vs the control communities for women ages 20–35 and 55–80, respectively . Table 11.10 Relationship of calcium content of drinking water to the rate of fractures in rural Iowa Ages 20-35 Number of women with fractures Total number of women Ages 55-80 Number of woemn with fractures Total number of women Control 3 37 Control 11 121 High calcium 1 33 High calcium 21 148 13.1 What test can be used to compare the fracturerates in these two communities while controlling for age? 13.2 Implement the test in Problem 13.1, report a p-value, and make a conclusion on relationship between drinking water calcium concentration and rate of fracture based on the p-value.arrow_forward
- A study was performed looking at the risk of fractures in three rural Iowa communities according to whether their drinking water was “higher calcium,” “higher fluorides,” or “control” as determined by water samples. Table 11.10 presents data comparing the rate of fractures (over 5 years) between the higher-calcium vs the control communities for women ages 20–35 and 55–80, respectively . Table 11.10 Relationship of calcium content of drinking water to the rate of fractures in rural Iowa Ages 20-35 Number of women with fractures Total number of women Ages 55-80 Number of woemn with fractures Total number of women Control 3 37 Control 11 121 High calcium 1 33 High calcium 21 148 13.1 What test can be used to compare the fracturerates in these two communities while controlling for age? 13.2 Implement the test in Problem 13.1, report a p-value, and make a conclusion on relationship between drinking water calcium concentration and rate of fracture based on the p-value. 13.3…arrow_forwardUse the information below to answer Questions #16 - 22. The article "Probabilistic Fatigue Evaluation of Riveted Railway Bridges" (J. of Bridge Engr., 2008: 237- 244) suggested the exponential distribution with A = 9 as a model for the distribution of stress range (MPa) in certain bridge connections. What value separates the highest 2% of the stress ranges from the remaining 98%? Round to four decimal places as needed.arrow_forwardIn the article “The World's Longest Continued Series of Sea Level Observations” (M. Ekman, Paleogeography, 1988:73–77), the mean annual level of land uplift in Stockholm, Sweden, was estimated to be 4.93 ± 0.23 mm for the years 1774–1884 and to be 3.92 ± 0.19 mm for the years 1885–1984. Estimate the difference in the mean annual uplift between these two time periods, and find the uncertainty in the estimate.arrow_forward
- a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?arrow_forwardAs the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article: YF: 28, 34, 32, 27, 28, 32, 31, 35, 32, 28 OF: 19, 14, 21, 13, 12 Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use ?1 for younger females and ?2 for older females.) H0: ?1 − ?2 = 10Ha: ?1 − ?2 > 10H0: ?1 − ?2 = 10Ha: ?1 − ?2 < 10 H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0 Calculate the test statistic and determine the P-value. (Round your test…arrow_forwardUse the information below to answer Questions #16 - 22. The article "Probabilistic Fatigue Evaluation of Riveted Railway Bridges" (J. of Bridge Engr., 2008: 237- 244) suggested the exponential distribution with A = 9 as a model for the distribution of stress range (MPa) in certain bridge connections. Find the mean. Round to four decimal places as needed.arrow_forward
- Find the median for each of the following pdfs: frV)=(0+1)y®, Osys1 for 0>0arrow_forwardIn the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean λ = 3. The profit per foot when the rope is sold is given by X, where X = 60 - 4Y - y². Find the expected profit per foot. $ per footarrow_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_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill