Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.7, Pr(B) = 0.5, Pr(C) = 0.2.
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- When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinneb. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.6
- The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. A) find the mean of p b)find the standard deviation of p c)Compute an approximation for P≥p0.0125, which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.A veterinary hospital manager suspects that pet owners visit the veterinarian less than 3 times a year. To verify this suspicion, he hires a market research agency that takes a random sample of 64 clients and asks them the number of times they go to the veterinarian per year. The decision the market researcher makes is that if 2.8, then he will have sufficient evidence to say that the manager's suspicion is true. Assume that the frequency of visiting the veterinarian has a standard deviation of 1.02. a) Write the null hypothesis and the alternative hypothesis in this case. b) What is the rejection region used by the investigator? c) What is the probability of type I. error if this rejection region is used? d) If the true mean of the number of visits to the veterinarian is = 2.7, what is the probability of type II error? e) If the true mean of the number of visits to the veterinarian is = 2.7, what is the power of the test? f) If the true mean of the number of visits to…
- Let A, B and C be events from a common sample space such that: P(A) = 0.72, P(B) = 0.56, P(C) =0.25, P(ANB) = 0.42. P(ANC) = 0.18, P(BOC) =0 %3D Compute P(AUBUC).3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following (refer Table 4): Employees y X1 X2 1 100 9 6 2 90 4 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 2 4 8 30 2 2 (a) Run a regression analysis based on the data in Table 4 using Mic. Office EXCEL. Based on theoutput, propose a regression equation that can be used to predict paralegal GPA.(b) Interpret the coefficient value of each independent variable in the constructedmodel(c) Is each independent variable sharing a significant linear relationship with the dependent variable?Verify at 0.05 level of significance. Make your conclusion based on the p-value in the EXCEL output.
- Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E4} B = {E2, E3} C = {E2, E4, E5}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find P(A ∪ B). P(A ∪ B) = Are A and B mutually exclusive? They mutually exclusive. (c) Find AC. (Enter your answer in set notation.) AC = Find CC. (Enter your answer in set notation.) CC = Find P(AC) and P(CC). P(AC) = P(CC) = (d) Find A ∪ BC. (Enter your answer in set notation.) A ∪ BC = Find P(A ∪ BC). P(A ∪ BC) = (e) Find P(B ∪ C). P(B ∪ C) =(b)A random sample of twelve students were chosen, and their midterm test score ( y), assignment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 65 8 74 50 7 76 55 5 90 65 2 85 55 6 87 70 3 94 65 2 98 70 5 81 55 4 91 70 3 76 50 1 74 55 4 (i)What is the fitted multiple linear regression equation of the form ˆy = b0 + b1x1 + b2x2? (ii)From part 6(b)(i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes. (iii)Assume that the data on ( y, x1, x2) above in 6(b) is inputted into SPSS, with the following results: ANOVA Source SS df MS F…