Compute the following binomial probability directly from the formula for b(x; n, p). Express your answers to 4 decimal places (0.xxxx). b(3; 8, .7) = P(X ≥ 1) when n = 8 and p = 0.10.
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- Consider the following PMF function: P(X=x)=x/15 for x=1,2,3,4,5 What is the probability that X is odd?T15 Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.4. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)The probability that a battery will last 10 hr or more is 0.8, and the probability that it will last 15 hr or more is 0.11. Given that a battery has lasted 10 hr, find the probability that it will last 15 hr or more. (Round your answer to three decimal places.)
- an unfair coin with Pr[H]=0.85 is flipped. If the flip results in a head, one student is selected at random from a class of 4 girls and 6 boys. If the flip results in a tail, one student is selected from a different class containing 7 girls and 3 boys. Find the probability that the flip resulted in heads given that a boy was selected.Suppose that 0.7% of male professional golfers use steroids, and that Max is a male professional golfer who has been randomly selected to take a drug test. The test he has been asked to take has a false positive rate of 1% and a false negative rate of 10%. Use Bayes’ rule to calculate the probability that Max actually uses steroids if he tests positive for steroid use. Give your answer as a decimal precise to three decimal places.Match the following questions with the correct answers. A. 24 B. 0.0929 C. 2 D. 154 E. 3/4 F. 120 select select select select select select 1. If X220, the probability that a man aged x marries at time t from the present is 15dt/(t+x)2. Find the probability that a person aged 20 eventually marries. 2. If X is the number of 6's which appear when 72 dice are thrown, what is the expected value of X²? 3. Suppose only 12% of men in ancient Greece were honest. What is the probability that the first honest man Diogenes Jencounters will be the third man he meets? 4. Find the expected value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 5. Find the variance value of the number of times one must throw a die until the outcome 1 has occurred 4 times? 6. If for a Poisson distribution 2f(0)+f(2)=2f(1), what is the variance of the distribution?
- Compute the probability of X successes using the binomial formula. Round your answers to three decimal places as needed. n= 1, p= 0.29, X=0Find the value of X (Left Tailed Probability of 0.5) for v1 = 10 and v2 = 20 degrees of freedom.The probability that someone passes the road test to get a driver's license is 0.55. Let N represent the number of road tests a person must take to get his/her driver's license. Find P(N < 6). (Round your answer to 3 decimal places).
- Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…Help
