Problem #1: A box consists of 12 components, 7 of which are defective.Problem #1(a):Problem #1(b):(a) Components are selected and tested one at a time, without replacement, until a non-defective component isfound. Let X be the number of tests required. Find P(X= 3).(b) Components are selected and tested, one at a time without replacement, until two consecutive non defectivecomponents are obtained. Let X be the number of tests required. Find P(X= 5).Round your answer to 4 decimals.Round your answer to 4 decimals.

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Answered: Problem #1: A box consists of 12…

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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mathematical statistics. Problem 2.
6&13
Suppose the entire cola industry produces only two colas. Given that a person last purchased cola 1, there a 70% chance that her next purchase will be cola 1. Given that a person last purchased cola 2, there is an 75% chance that her next purchase will be cola 2. Suppose that each customer makes one purchase of cola during any week (52 weeks=1 year). Suppose there are 150 million customers. One selling unit of cola costs the company $0.5 to produce and is sold for $2. For $200 million per year, Britney Spears (by an advertising song) guarantees to decrease from 30% to 15% the fraction of cola 1 customers who switch to cola 2 after a purchase. Should the company that makes cola 1 hire Britney Spears?
Problem #3: A high-risk group of 808 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 328 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 15 of the vaccinated people and 33 of the nonvaccinated ones later got the disease. Problem #3(a): Problem #3(b): Problem #3 (c): Problem #3 (d): Problem #3(e): We wish to test the hypothesis that the probability of getting type B hepatitis is different (higher or lower) for people who were vaccinated compared with people who were not, using the 5% significance level. (a) If we use the contingency table method to test this hypothesis, find the 4 values in the expected table. (b) Find the value of the test statistic (using the contingency table method). (c) Find the critical value (using the contingency table method). (d) Using the z-test for proportions, find the value of the test statistic (and verify x², when…
Suppose there are four cities at locations x1 = 2; x2 = 5; x3 = 9, and x4 = 11, requiring respectively Ni = 6; 2; 3; 7 visits, respectively. Suppose that the cost-per-mile to ship goods is $4 between x1 and x2, but $8 between x2 and x3, and $10 between x3 and x4. What is the cost of keeping the PDC at x = 6? What about at x = 10?
Problem#1: Exercise and diet are being studied as possible substitutes for medication to lower blood pressure. Three groups of subjects will be used to study the effect of exercise. Group 1 is sedentary, while group 2 walks and group 3 swims for 1 hour a day. Half of each of the three exercise groups will be on a salt-free diet. An additional group of subjects will not exercise or restrict their salt, but will take the standard medication. Use Z for sedentary, W for walker, S for swimmer, Y for salt, N for no salt, M for medication, and F for medication free (a) Show all of the elements of the sample space S. (b) Given that A is the set of nonmedicated subjects and B is the set of walkers, list the elements of A ∪ B. (c) List the elements of A ∩ B.
TRUE (1) OR FALSE (2) According to Statistics South Africa (2011), the total human population of KaNgove, a village in Giyani (South Africa), is 6376, while the total number of households is 1545. In this study, the population unit is the households since the study seeks to study indigenous systems of households. Based on the facts above: The population size of this study will be (N=6376)? TRUE / FALSE The population size of this study will be (N=1545)? TRUE/FALSE The sample size will be n=155? TRUE/FALSE
A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r 5 P(#2 fails | #1 fails). P(#2 fails) = q. If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?

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