Probability Homework Problem 1 We draw the top 7 cards from a well-shuffled standard 52-card deck. Find the probability that: (a) The 7 cards include exactly 3 aces. (b) The 7 cards include exactly 2 kings. (c) The probability that the 7 cards include exactly 3 aces. or exactly 2 kings, or both.
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- Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? In a sample of 123 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 261 women with cosmetic dermatitis from using mascara, 27 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. b. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. c. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow ormascara) is 0.15. Can you determine which group isreferenced?Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? In a sample of 126 women with cosmetic dermatitis from using eye shadow, 11 were diagnosed with a nickel allergy. In a sample of 266 women with cosmetic dermatitis from using mascara, 26 were diagnosed with a nickel allergy. Use this information to complete parts a through c below. Question content area bottom Part 1 a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. The 95% confidence interval for eye shadow is enter your response here,enter your response here.Consider a screening system that analyzes the luggage that is being loadedto a plane. Each package first goes through a screening device. If it passes the test there, then it is loaded to the plane. If it does not, the package goes to a second screening device. The procedure is similar for the second device: if the luggage passes the test, it is loaded to the plane, if it fails, it issent to a third device. Packages that passes the test at third device are loladed to the plane, the ones that fail are taken paprt and not loaded to the plane.The screening devices i = 1; 2; 3 are not perfect. For each device, there are two risks:– With probability pi, each device erroneously passes a bag that is dangerous, given that previous devices have correctly rejected the bag.– With probability qi, each device erroneously fails a harmless bag that previous devices have also erroneously failed.Assume that pi; qi > 0 What is the probability that a dangerous package will be loaded to the aircraft?…
- A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of adults in the country who think that their taxes will be audited is not enter your response here%. B. enter your response here% of adults in the country think that their taxes will be audited. C. Less than enter your response here% of adults in the country think that their taxes will be audited. D. At least enter your response here% of adults in the country think…A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 28% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. ______% of adults in the country think that their taxes will be audited. B. The percentage of adults in the country who think that their taxes will be audited is not ______%. C. Less than ______% of adults in the country think that their taxes will be audited. D. At least ______% of adults in the country think that their taxes will be audited. (b) Find the critical value(s) and identify the rejection region(s). (c)…A scientist is interested in whether stretching before running 5 kilometers will improve a runner’s time. The scientist decides that an experimental study is the best method to use to answer the question. One group of runners will run a 5-kilometer race without stretching, and a second group of runners will follow a specific stretching routine before running the race. The finishing times will be recorded, along with the group type for each runner. Assuming this group is representative of all adults who followed a specific stretching routine before running, use a normal distribution to estimate the probability that a randomly-selected adult could complete the race in fewer than 20 minutes after stretching. **THIS IS THE FULL QUESTION AND THIS IS NOT GRADED ***
- For a parrallel structure of identical components the system can succeed if one of the component succeeds. Assume that the components fail independently of each other and that each component has a 0.11 probability of failure. a.) would it be unusual to observe one component fail? it ____ be unusual to observe one component fail since the probability that the component fails, ___ is ___ than 0.05. It ___ be unusual to observe two components fail since the probability that two components fail __ is __ than 0.05 b.) what is the probability that a parrallel structure with 2 identical components will succeed? c.) how many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?A research center claims that at least 28% of adults in a certain country think that their taxes will be audited. In a random sample of1000 adults in that country in a recent year, 23%say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. nothing% of adults in the country think that their taxes will be audited. B. Less than nothing% of adults in the country think that their taxes will be audited. C. At least nothing% of adults in the country think that their taxes will be audited. D. The percentage of adults in the country who think that their taxes will be audited is not nothing%. Let p be the population proportion of…A researcher is interested in understanding how the flexibility of vacation policies at a company influence employee satisfaction with their job. Company 1, Vance Refrigeration, has a 2 week vacation policy in which employees can take those 2 weeks at any time during the year. Company 2, Dunder Mifflin Paper Company, has a 2 week vacation policy in which employees can only take vacation days during specific pre-approved times of year. What is the confound?
- Three components are connected to form a system asshown in the accompanying diagram. Because the componentsin the 2–3 subsystem are connected in parallel, thatsubsystem will function if at least one of the two individualcomponents functions. For the entire system to function,component 1 must function and so must the 2–3 subsystem. The experiment consists of determining the condition ofeach component [S (success) for a functioning componentand F (failure) for a nonfunctioning component].a. Which outcomes are contained in the event A thatexactly two out of the three components function?b. Which outcomes are contained in the event B that atleast two of the components function?c. Which outcomes are contained in the event C that thesystem functions?d. List outcomes in C9, A ø C, A ù C, B ø C, andB ù C.A medical researcher says that less than 74%of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 600adults in that country, 71% think that healthy children should be required to be vaccinated. At α=0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 andHa. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) Fill the percentage on the correct answer A. % of adults in the country think that healthy children should be required to be vaccinated. B. Less than %of adults in the country think that healthy children should be required to be vaccinated. C. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %. D. More than…*Please work with your version, don't copy from other sources use table t in doing it 1. A testing engineer is stress testing an Application Programming Interface (API) made by his company on twenty servers from two different vendors. The maximum number of hits from each server from each vendor is as follows (in thousands):Server Vendor A: 42.1 ; 41.3 ; 42.4 ; 43.2 ; 41.8 ; 41.0 ; 41.8 ; 42.8 ; 42,3 ; 42.7Server Vendor B: 42.7 ; 43.8 ; 42.5 ; 43.1 ; 44.0 ; 43.6 ; 43.3 ; 43.5 ; 41.7 ; 44.1It is known that the two stress test data are normally distributed with the same variance.a. Compute the 99% two-sided confidence interval for the difference in the mean number of hits from the servers of the two vendors.b. Compute the 97.5% upper confidence interval (97.5% upper confidence interval) for the difference in the average number of hits from the servers of the two vendors.c. Compute a lower confidence interval of 90% for the difference in the average number of hits from the servers of the…