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- The expected life of a certain component in a mechanism is treated as a random variable having a gamma distribution with a = 3 and ß = 2. The average expected life of such component is 12 months, what is the probability that this component can have a greater than average expected life?In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 141. What is the probability that the sample proportion will be at most 4 percent more than the population proportion? (Enter your answer as a number accurate to 4 decimal places.)You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.67. Your sample data produce the test statistic z=3.203. Find the p-value accurate to 4 decimal places. You are conducting a study to see if the probability of catching the flu this year is significantly different from 0.33. Your sample data produce the test statistic z=1.84 Find the p-value accurate to 4 decimal places.
- The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?Researchers developed a "cat IQ test" and find that the population of cats in the United States has a mean score of u = 25 on this test with a standard deviation of g = 3. You decide to test a sample of n = 45 cats to do some research about whether some breeds are smarter. You collect your sample of n = 45 cats and find their mean cat IQ is M = 25.5. What is the probability of this sample? That is, what is p(M>25.5)?Bernoulli process: i.Draw the probability distributions (pdf) for X∼bin (8, p) (x) forp = 0.25, p = 0.5, p = 0.75, in each diagram.ii.What kind of effect has a higher value on the graph , compared to a lower value? iii.You should strike a coin8gonger. You win if there are precise4 or precise5 coins, but otherwise lose. You can choose between three different coins, medpn = P (coin) respectively p1 = 0.25, p2 = 0.5, andp3 = 0.75. Which of these coins gives you the highest probability of winning?
- 6. For an insurance coverage, claim counts follow a binomial distribution with m = 4. q varies by insured with the following probabilities: 0.1 0.2 0.3 Probability 0.5 0.25 0.25 An insured submits 0 claims in the first year and 3 claims in the second year. Calculate the predictive probability of the same insured submitting 0 claims in the third year.Assume that the probability of a 25-year-old male living to age 26, based on mortality tables, is 0.993. If a 16,000 dollar one-year term life insurance policy on a 25-year-old male costs 100 dollars, what is its expected value? What is the expected value? The expected value is dollars.A book seller has the following schedule of weekly. demand for the book "Elementary Quantitative Methods" No. of copies on demand : Probability : 100 200 300 400 500 .02 .05 .09 .12 .20 .15 Find the expected number of copies demanded per week.
