In order to ensure the quality of concrete material used in a reinforced concreteconstruction, concrete cylinders are collected at random from concrete mixes delivered to theconstruction site from a mixing plant. Past records of concrete from this same plant show that75% of concrete mixes are good or of satisfactory quality. To further ensure that the concretedelivered on site is of good quality, the engineer requires that one concrete cylinder among thosecollected each day be tested (after 14 days of curing) for minimum compressive strength. Thereliability of the test method is only 85%, meaning that the probability a good quality concretepass the test is 0.85, or that a poor quality cylinder can pass the test is 0.15. It is desired to obtainthe following information:1. If a concrete cylinder passed the test, what is the updated probability that good-qualityconcrete was delivered at the site; and2. If a second cylinder is tested and also passes the test, what is the updated probabilitythat good-quality concrete was delivered at the site.

Given Information: 75% of concrete mixes are good or satisfactory quality. The probability a good…

Answered: In order to ensure the quality of…

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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A state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water specimens taken from a river at a specific location during the low-water season (July) gave readings of 4.8, 5.2, 4.8, 4.9, 4.9, and 4.6 ppm of dissolved oxygen. Do the data provide sufficient evidence to indicate that the dissolved oxygen content is less than 5 ppm? Test using ? = 0.05. a) state null and alternate hypotheses b) state the test statistic c) state the rejection region d) state the conclusion
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
The foundation of a building is designed to be supported by 100 piles with a capacity of 80 tons each. 9 pilesdriven into the ground layers supported at the Ras tgele points were loaded until migration occurred in each pile and the results given in the table below were obtained. Test Pile Pile Capacity (tons) 1 90 2 75 3 95 4 90 5 88 6 92 7 78 8 85 9 88 a) Calculate the average and standard deviation for the individual pile capacity to be used in construction. b) At a 5% significance level, based on the results of 9 test piles, are the manufactured piles acceptable? The zero hypothesis would indicate that the average pile capacity is 80 tons. Determine the 95% confidence interval for the average pile capacity. c) d) Repeat the calculations you made manually above withR. Provide the R code and its result separately as the answer to this option.
Food deserts have become a particularly hot topic in the public health community as anexplanation for a variety of negative health outcomes in disadvantaged areas. Aresearcher is interested in comparing the average shelf space provided by supermarkets,convenience stores, and corner stores in two different communities in order to address thegrowing concern for food deserts. Assume the following table reports the summary statistics for shelf space dedicated to fresh fruits and vegetables (meters) obtained from SRSs of a variety of different stores that supply groceries from each community. Community Average Shelf Space For Fruits and Veg. (m) Sample Standard Deviation Sample Size "Food Desert" 13.7 2.4 12 Other Community 89.4 14.6 14 a) Carry out the appropriate statistical test in order to determine if there is a significant difference in mean shelf space between the two communities at the alpha level of 0.05. Assume all conditions for the test are met. Do not assume equal…
The heights of men in a certain city are normally distributed with a mean of 275 cm and a variance of 25cm. Compute the minimum height for the top sixteen percent of the men in the city.
In an investigation of possible brain damage due to alcoholism, an x-ray procedure known as a computer assisted tomography (CAT) scan was used to measure brain densities in 8 chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, race, height, and other factors. The brain density measurements on the alcoholics and the matched controls are recorded below. Assume normally distributed data here. Use an appropriate test to determine whether there is evidence of diminished brain density due to chronic alcoholism.
Big Hitter is a manufacturer of golf products in the United States and Canada. One of the golf accessories it produces at its plant in Winnipeg, Manitoba, Canada, is plastic golf tees. The injector molder produces golf tees that are designed to have an average height of 66mm. To determine if this specification is met, random samples are taken from the production floor. One sample is contained in the file labeled THeight. Determine if the process is not producing the tees to specification. Use a significance level of 0.01. If the hypothesis test determines the specification is not being met, the production process will be shut down while causes and remedies are determined. At times this occurs even though the process is functioning to specification. What type of statistical error would this be? THeight 67.05 66.61 65.58 65.26 66.23 65.69 64.90 67.67 65.77 66.13 67.43 65.77 66.46 66.31 66.39 66.10 66.58 66.98 67.13 65.81 66.86 66.26…
The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce…

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