What is the probability that a customer has to wait more than 15 minutes to get his service completed in an M/M/1 queueing system, if λ = 6 per hour and = 10 per hour?
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- A group of investigators wishes to explore the relationship between the use of hair dyes and the development of breast cancer in females. A group of 100 beauticians 40–49 years of age is identified and followed for five years. After five years, 20 new cases of breast cancer have occurred. Assume that breast cancer incidence over this time period for average American women in this age group is 30/100. We wish to test the hypothesis that using hair dyes decrease the risk of breast cancer. Compute p-value (The answer is Not 0.0021) Please choose answer from these two following multiple choice. a) 0 b) 47.6190One mechanism formed by two identical components of type A, arranged in series, has a reliability of 60% after 1000 hours. A new component B is added in parallel in order to improve the reliability of the device up to 90% after 1000 hours. What should be the reliability of component B after 1000 hours?i need the answer quickly
- A study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ACBG = y, summary values are n = 26, Ex; = 1620, 2(x₁ - x)² = 3756.96, y₁ = 281.9, (y₁ - y)² = 465.34, and Ex,y; = 16,733. (a) Compute a 90% CI for the true correlation coefficient p. (Round your answers to four decimal places.) (b) Test Ho: p = -0.5 versus H₂: P < -0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = State the conclusion in the problem context. O Reject Ho. There is no evidence that p < -0.5. O Fail to reject Ho. There is evidence that p < -0.5. O Reject Ho. There is evidence that p < -0.5. O Fail to reject Ho. There is no evidence that p < -0.5. (c) In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by…Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 94 percent reliable, this means that the test will yield an accurate positive result in 94% of the cases where the disease is actually present. Gestational diabetes affects 4+1 percent of the population in our patient’s age group, and that our test has a false positive rate of 4+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? What is the probability of having the disease given that you test positive? If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? What is the…
- Consider a two component parallel system in which both components have times to failure and times to 0.0024 f/hr and µ1 = = 0.001 f /hr, 12 repair that are exponentially distributed. The data is 1, 0.003 r/hr and µ2 = 0.005 r/hr. Evaluate the reliability or probability of success for a mission of 1000 hr. (hint: form a history for each component using the data for failure rate and repair rate)You are an econometrician working in the Ministry of Finance in Trinidad and Tobago and using a database consisting of 108 monthly observations on automobile accidents for Trinidad and Tobago between January 2011 and December 2019, you estimate the following model: log( totacc,) = B, + Bit + B2feb, + ßzmar.. + B12dec, + µe where totacc is the total number of accidents, t is time (measured in months), and feb,, mar,, dec, are dummy variables indicating whether time period t corresponds to the appropriate month. You obtain the following OLS results: Number of obs F( 12, Prob > F df 108 31.06 0.0000 0.7969 Source I MS 95) Model | 1.00244071 Residual | .255496765 12 .083536726 95 .00268944 R-squared Adj R-squared = 0.7712 Root MSE Total | 1.25793748 107 .011756425 - .05186 ltotacc | Coef. Std. Err. t P>It| [958 Conf. Interval] .0024274 -.0912208 .031287 .0027471 .0001611 .0244475 .0244491 17.06 0.000 .0030669 .0058479 .1283621 feb | -.0426865 mar | apr | may | jun | jul | aug | sep I oct I…A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At a = 0.10, is there enough evidence to support the researcher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Male 1 2 4 6 7 8 9 10 Sprint time (without nap) Sprint time (with nap) 4.07 3.95 3.95 4.04 4.02 | 4.09 4.06 3.96 3.95 3.93 3.92 3.86 3.88 3.97 4.01 4.00 3.90 3.82 3.86 3.80 A. t 1.383 C. t (c) Calculate d and sg. d= j = 0.1 (Round to three decimal places as needed.) Calculate sa. = 0.045 (Round to three decimal places as needed.) (d) Find the standardized test statistic t. t = 6.666 (Round to three decimal places as needed.) (e) Decide…
- Assume a single server queueing system with exponential inter-arrival times, and service times. Assume that the expected inter-arrival time is 10 minutes, and the expected service time is 7.5 minutes. We are interested in the expected time the customers spend waiting in queue (in minutes). Develop a Monte Carlo simulation model to estimate Wg Calculate W (expected wait time in queue), and compare it with the previous resultA problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.