**Engine Failure Rates and Probability Calculation**In an article published in 2012 at Telegraph.co.uk, Warranty Direct provided engine failure rates for various car brands based on their database of UK direct consumer warranties. The known failure rates are listed below:- Hondas failed at a rate of 1 in 344.- Fords failed at a rate of 1 in 80.- Audis failed at a rate of 1 in 27.Suppose at a particular dealer:- Hondas account for 20% of sales,- Audis account for 30% of sales, and- Fords account for 50% of sales.Assuming the engine failure rates apply to these vehicles, we are to determine the probability that a randomly selected vehicle from this dealer will experience engine failure.To solve this, we use the law of total probability. The formula is:\[ P(\text{Engine Failure}) = P(\text{Engine Failure | Honda}) \times P(\text{Honda}) + P(\text{Engine Failure | Audi}) \times P(\text{Audi}) + P(\text{Engine Failure | Ford}) \times P(\text{Ford}) \]Given:- \( P(\text{Engine Failure | Honda}) = \frac{1}{344} \)- \( P(\text{Engine Failure | Audi}) = \frac{1}{27} \)- \( P(\text{Engine Failure | Ford}) = \frac{1}{80} \)And,- \( P(\text{Honda}) = 0.20 \)- \( P(\text{Audi}) = 0.30 \)- \( P(\text{Ford}) = 0.50 \)Substituting these values into the formula:\[ P(\text{Engine Failure}) = \left(\frac{1}{344}\right) \times 0.20 + \left(\frac{1}{27}\right) \times 0.30 + \left(\frac{1}{80}\right) \times 0.50 \]Calculate each term:\[ \frac{1}{344} \times 0.20 = 0.0005814 \]\[ \frac{1}{27} \times 0.30 = 0.0111111 \]\[ \frac{1}{80} \times 0.50 = 0.00625 \]

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The control department of a light bulb manufacturer randomly picks 4400 light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is 1% . When 1.5% or more of the light bulbs in the sample of 4400 are defective, the control unit calls repair technicians for service. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p , where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction. (b)Find the standard deviation of p . (c)Compute an approximation for P≥p0.015 , which is the probability that the service technicians will be called even though the system is functioning properly. Round your answer to four decimal places.
The table below shows the alcohol consumption per capita for seventeen high-income countries in 2000 according to https://ourworldindata.org. Country Liters of Alcohol Consumption per Capita in 1980 Australia 9.7Austria 11.1Belgium 11.5Canada 7.6Denmark 9.8Finland 5.1France 13.3Germany 12.7Italy 10.8Japan 6.5Netherlands 8.6New Zealand 9.1Norway 5.2Sweden 5.9Switzerland 11.4United Kingdom 8United States 7.7 1) Calculate the mean, median, mode, and standard deviation of the liters of alcohol consumption per capita for these 17 countries. Use your TI-84 calculator or Excel as necessary. If you calculate them by hand, include your work (neatly written on a separate sheet of paper!!). If you use Excel, include the Excel worksheet. If you use your TI-84, show what you’ve entered and the results you get. (You could take photos of your calculator and include those if you’d rather.)Mean = _______________________ (Round to 1 decimal place.)Median = ______________________Mode(s) =…
A certain medical school accepts only 8% of applicants. A prep program claims that their students are admitted to this medical school at a higher rate. To test their claim at the 10% significance level, we select at random 144 students from the prep program (who all apply to this medical school), and we compute p, the proportion of the sample who are admitted to the medical school.
In late July 2016, the Ohio Department of Health collected vials of water from 12 beaches on Lake Erie to investigate water quality. Those vials were being tested for E. coli bacteria which are found in human and animal feces and can cause illness and disease, should a swimmer accidentally ingest some water. These beaches had been found to be safe earlier in the summer with E. coli counts, on average of 88 per 100-millileter vial (about 3.4 ounces). However, E. coli counts can change due to weather and other variables. Experts consider it unsafe if a vial contains more than 88 E. coli bacteria. The mean E. coli count in the 12 vials was found to be 113.75 with a standard deviation of 93.9. Is this evidence that the water is unsafe? Test at the 1% level of significance. a) State the hypotheses. b) Find the test statistic and p-value. c) Based on your p-value, state whether or not you will reject the null hypothesis and a statement of your findings, relating back to the problem.
Answer A, B1, and B2: A. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population. B. Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level…
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better? A) There is convincing evidence because the interval is entirely above 0. B) There is not convincing evidence because the sample sizes are too small. C) There is convincing evidence because the number of clothing items receiving a…

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