Find the probability of x successes in 100 Bernoulli trials with probability p = 1/5 of success (a) if x = 25; (b) if x = 21.
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- 8 Julia is waiting for either of the two buses to her destination, and waiting times for those two different buses follow independent exponential distributions with mean 3 minutes and 7 minutes. Assuming she would get on the bus that comes first, what is her expected waiting time?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.It is known that in a certain town 30% of the people own an Kpfone. A researcher asks people at random whether they own an Kpfone. The random variable X represents the number of people asked up to and including the first person who owns an Kpfone. Determine that P(X <6).
- I need help with all parts of this question 8Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). DetermineAssume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. The probability of surviving 1 year after being…
- If X is exponentially distributed, prove that the probability that X exceed its expected value is less than 0.5A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n=1100n=1100 registered voters and found that 570 would vote for the Republican candidate. Let pp represent the proportion of registered voters in the state who would vote for the Republican candidate.We test H0:p=.50H0:p=.50Ha:p>.50Ha:p>.50 (a) What is the zz-statistic for this test? (b) What is the P-value of the test?Compute the power of the test if the researcher uses a sample of n = 4 individuals. The power for the test is the probability of obtaining a z-score than , which corresponds to p = Thus, the power of the test is %. Compute the power of the test if the researcher uses a sample of n = 25 individuals. The power for the test is the probability of obtaining a z-score than which corresponds to p = Thus, the %3D power of the test is 이0.
- A gambler simulates a new card game on a computer. Out of 500 trials he wins 200 times. So he calculates P(winning) = 200/500 = 0.40. Why is this only an estimate of the true value of P(winning)? A. There are more than 2 events B. The outcomes are not equally likely C. His estimate is not rounded to 3 decimal places D. If he were to do a different set of 500 trials, he might win 180 times and calculate a different value of P(winning)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.…An experiment consists of flipping a weighted coin with Pr[H]=0.8Pr[H]=0.8. The experiment ends when either heads is flipped 3 times or tails is flipped. What is the probability that heads was flipped at least once given the coin was flipped at most two times?
