The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft.0.734 0.8620.878 0.901 0.922 0.943 0.961 1.0091.040 1.047 1.083 1.115 1.137 1.159 1.244 1.352USE SALT(a) Compute and compare the values of the sample mean x and median X. (Round your mean to four decimal places.)x = 1.0236X flight hours/104X = 1.0240X flight hours/104(b) By how much could the largest sample observation be decreased without affecting the value of the median? (Enter your answer to three decimal places.)0.316X flight hours/104

Given data: Sample size = 16 To find: 1.sample mean 2. Median

Answered: The propagation of fatigue cracks in…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. A. Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…
Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Find a 95% confidence interval for the mean long-term measurement for those with short-term measurements…
Example 27 : It is desired to estimate the mean number of hours of continuous use until a centain computer will first require repairs. If it can be assumed that o= 48 hours. How large the sample will be needed so that one will be able to assert with 90% confidence that the sample mean is off by at most 10 hours.
There has been a long-held belief that births occur more frequently in the "small hours of the morning" than at any other time of day. Sutton [1945] collected the time of birth at the King George V Memorial Hospital, Sydney, for 2654 consecutive births. (Note: The total number of observations listed is 2650, not 2654 as stated by Sutton.) The frequency of births by hour in a 24-hour day is listed in Table 3.16. (a) Sutton states that the data "confirmed the belief ... that more births occur in the small hours of the morning than at any other time in the 24 hours." Develop a graphical display that illustrates this point. (b) Is there evidence of Sutton's statement: "An interesting point emerging was the relatively small number of births during the meal hours of the staff; this sug- gested either hastening or holding back of the second stage during meal hours"? Table 3.16 Frequency of Birth by Hour of Birth Time Births Time Births Time 6-7 pm 7 pm 8 pm 9 pm 10 pm 11 pm 12 am 1 am 92 102…
A research center claims that 25% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 27% say that they would travel into space on a commercial flight if they could afford it. At a = 0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. INU TIIUIE uIOan 0 UI auuiS I uIE UUUU y vwuuIu uavci IU apauc Un a uUITIIGI LIaI Iyntrncy couIu anuIu I. O D. At least % of adults in the country would travel into space on a commercial flight if they could afford it. Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State H, and Ha. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) O A. Ho: p O B. Ha: ps OC. Ho: p> Hai p= Hai p> Ha: ps O D. Ho: pe O E. Hg:…
A machine operator is required to reach between the tools of a vertical hydraulic press between each cycle of the press. Under fault conditions, the operator is at risk from a crushing injury due either (a) to the press tool falling by gravity or (b) to an unplanned (powered) stroke of the press. The expected frequencies of the failures that would lead to either of these effects are given in the table below: Frequency (per year) Effect 0.2 a 0.1 0.1 0.05 Failure type Flexible hose failure Detachment of press tool Electrical fault Hydraulic valve failure (i) a b a or b Given that the operator is at risk for 20 per cent of the time that the machine is operating, construct and quantify a simple fault tree to show the expected frequency of the top event (a crushing injury to the operator's hand).
9.4 A flange bolt wears out because of fatigue in accordance with the lognormal distribution with MTTF 10,000 hr and s = 2.00. If preventive maintenance consists of period- ically replacing the bolt, what is the reliability at 550 hr with and without preventive maintenance? Assume that the bolts are replaced every 100 operating hours. =
30 of 68 ge 13. Your teacl 11. A consumers group recently tested 100compact fluorescent light bulbs and recorded their lifetimes. The shows the boys ages chart shows the results. 2 to 20 years: Boys Body mass index-for-age Lifetime (h) Frequency Date Age Weight Stat 5000-6000 7 6000-7000 12 7000-8000 34 8000-9000 27 9000-10 000 10 *To Calculate BMI: Weight (kg or Weight (Ib) - Sta BMI 10 000–11 000 27 11 000-12 000 26 25- a) Make a box and whisker plot of the 24 23 data. 22 b) Make a histogram of the data and mark the quartiles on it. 21 20 19 c) Describe the middle 50% of the data. 18 17 d) Identify any outliers. 16 15 12 Agencies trocl o 1:
Poisoning by the pesticide DDT causes tremors and convulsions. In a study of DDT poisoning, researchers fed several rats a measured amount of DDT. They then made measurements on the rats’ nervous systems that might explain how DDT poisoning causes tremors. One important variable was the “absolutely refractory period,” the time required for a nerve to recover after a stimulus. This period varies normally. Measurements on four rats gave the following measurements (in milliseconds): 6, 1.7, 1.8, 1.9. Estimate the mean absolutely refractory period for all rats of this strain when subjected to the same treatment.
3. An experiment is conducted to measure the flex (amount of bending) in a thin composite beam when placed under a known load (force). Smaller beams made of the same material will then be used as springs to protect electronics. The manufacturer needs the beam to flex on average 5.0 mm, with 95 % of all samples having a flex between 4.7 mm and 5.3 mm. After testing the flex of 20 samples, the following numbers are found: (d) (e) 20 (f) (g) i=1 Each sample has the flex measured to the nearest 0.1 mm using electronic calipers. (a) What is the mean flex found using 20 samples? What is the sample standard deviation of flex four using 20 samples? What is the 95% confidence interval for an individual sample? (Not true mean this time!) That is, in what range would we expect the flex of 95 % of the samples to be found? x₁ = 102.2 mm 20 Σχι" = 523.7 mm2 Xi i=1 Does the set of samples used satisfy the desired failure rate? Explain the reasoning behind your answer. What percent difference is there…
QUESTION 4 A gambler is accused of using a loaded die, but he pleads innocent. A record has been kept of the last 60 throws. See the table below. There is disagreement about how to interpret the data and a statistician is called in. Observed Value frequency 1 9. 2 11 3 10 4 8 5 12 6. 10 Compute the value of x2. (Your answer should be an integer with no decimals.)

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