cle “Reliability of Domestic-Waste Biofilm Reactors” (J. of Envir. Engr., 1995: 785–790) suggests that substrate concentration (mg/cm3 )of influent to a reactor is normally distributed with μ = .30and σ= .06. a. What is the probability that the concentration exceeds .25? b. What is the probability that the concentration is at most .10? c. How would you characterize the largest 5% of all con

cle “Reliability of Domestic-Waste Biofilm Reactors” (J. of Envir. Engr., 1995: 785–790) suggests that substrate concentration (mg/cm3 )of influent to a reactor is normally distributed with μ = .30and σ= .06. a. What is the probability that the concentration exceeds .25? b. What is the probability that the concentration is at most .10? c. How would you characterize the largest 5% of all con

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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4. Let Z be the standardized normal variable, i.e. Z follows normal distribution with the meanμ = 0, and variance σ 2 = 1. Find the value of the following probabilities. In each case, sketch a curve and shade the area representing the probability.a. P(Z < −0.6) b. P(Z > −1.28) c. P(0.81 < Z < 1.94)
Recall that Benford's Law clalms that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The…
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.
b) i. Let Y be the mean of sample of size n from a normal distribution with mean μ and variance 100. Find n so that Pu-5<Ỹ < µ+5)= 0.954
ol 106. Use the two scenarios presented in Figure 7.12 to answer the following question about the two sources of variability in ANOVA. 3.5 3.0 2.5 2.0 1.5 (i) HA: P₁ P2 ‡ P3 (iii) HA not all proportions are equal to this po 1.0 Figure 7.12: Within vs Between Variability in ANOVA onnisth Scenario A L (d) Recall that, O 2 H 3 2.05 2.10 2.15 2.20 2.25 2.30 2.35 (ii) Ho: M₁ M₂ = μ3 sans are (iv) HA: not all means are equal 720 qeaoluet alt sot mol 4 mobor 2924 (6) 2 3 4 gob za aim onbala (1) di batt (9) w-qodt fonqtotal bac o2 (6) (Troy ote12. (0) (a) Which scenario provides stronger evidence that the difference in factor level means represents true differences in the population means? Explain why in your own words. Scenario B 1 = stogol 05 O 1 oftaltete fest out of sulav gris I (b) Which scenario exhibits more variability within each factor level? Is this measured by SSError or SSFactor? Agulow (c) Which scenario exhibits more variability between each factor level? Is this measured by…
3. Let X1,X2, ..,X, be a random sample form a normal distribution with E(X;) = µ;and Var(X;) = o². Assume s? = E(X;_ X)²/n and s3 = (n/(n – 1))s?. Questions: a. Compare between the estimators si and s?. b. Which one you preferred? What is (are) your reason(s). 4. Let X1,X2, . X, be a random sample form a uniform distribution, f(X)e = 0*(1– e)!-*; 0 < x < 1. Assume T1 = X1 and T, = (-)Ex;. %3D a. Check the unbiasedness property for T1 and T,. b. Find the MSE of T, and T,. Can you preferer one of them? Discuss your reasons. с. 5. Suppose that X, X2,. , X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+ X8); -1< X <1. Show that 3x is a consistent estimator of e.
3. Let X1, .… , Xn be a random sample. Find the mle of 0 for the cases that the population pdf/pmf is, f(r;:0) = 0, %3D otherwise
3. Computer chips often contain surface imperfections. For a certain type of computer chips, the probability mass function of the number of defects X is presented in the following table. x 0 1 2 3 4 5 P(x) 0.28 0.23 0.18.15 0.13 0.03 a) Find P(X ≤2). b) Find P(X> 1). c) Find the mean number of defects, μ d) Find the variance of the number of defects, o²
Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 10 drivers living on one particular street, 3 were involved in a car accident last year. If 10 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? O a. O b. O C. O d. 0.4435 0.9548 0.0541 0.0452
Contaminated water: Polychlorinated biphenyls (PCBS) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 80 has a sample mean of 1.90 parts per billion (ppb). Assume the population standard deviation is o = 0.26 ppb. Part 1 of 3 ▬▬ esc (a) Construct a 98% confidence interval for the PCB concentration. Use tables or technology. Round your answers to at least two decimal places. The confidence interval is 1.83 1.97 Part 2 of 3 Skip Part Check Type here to search 12 2 # * 3 14 $ 4 D Et % 5 6 & 7 4+ Save For Later © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center 55°F 8 9 ho Submit. ► 11 d 1 3/