c. If X has a geometric distribution with success probability p. Show that for any positive integer a P(X > a) = qª
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![c. If X has a geometric distribution with success probability p.
Show that for any positive integer a
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- The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $204. a. The lambda of this distribution is b. The probability that the cost is larger than $238 is P(x > $238) = c. The probability that the cost is less than $76 is P(x s $76) = d. The probability that the cost is between $185 and $244 is P($185 s x < $244) = e. The 61st percentile is cost of maintenance sRecall that 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. Now 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 = 215 numerical entries from the file and r = 50 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. (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5. What is the value of the sample test…1) Assuming 6 degrees of freedom, find the following probability. P(T > 1.7) = 2) Assuming 16 degrees of freedom, find the following probability. P(T < – 2.024) =
- A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table on the right shows the day of the week for which 777 randomly selected fatal bicycle accidents occurred. At. α=0.10, can you reject the claim that the distribution isuniform? Complete parts a through d below.Recall that 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. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.(i) Test the claim that p is more than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p > 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301 H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling distribution will you use? The…Let X be the number of blueberries on a muffin made by Michael, and denote by m to be its median. Charles suspects that Michael has been adding more blueberries than usual to his muffins. For some reason, he has kept meticulous records. The last 15 muffins Charles bought contained the following numbers of blueberries: 96 12 8 15 7 8 12 6 10 13 11 11 10 10 Charles would like to test Ho: m = 9 against H₁: m>9 at significance level a = 0.1. (a) Use the sign test to test the hypothesis. (b) Use the Wilcoxon sign-rank test to test the hypothesis. (Note: Assume that the distribution is continuous) (c) Use the t-test to test the hypothesis, assuming the underlying distribution is symmetric.
- A random sample of size n1 = 15 is selected from a normal population with a mean of 75 and a standard deviation of 9. A second random sample of size n2 = 9 is taken from another normal population with mean 69 and standard deviation 15. Let X1 and X2 be the %3D two sample means. Find: (a) The probability that X - X2 exceeds 3. (b) The probability that 4.9 < X – X2 < 5.9. Round your answers to two decimal places (e.g. 98.76). (a) i (b)Find the highest possible value for x in the set 8.2 7.7 6 4.8 8.2 5.8 9.2 7.3 6.2 8.1 5.5 and x such that the mean of these scores is 7. show complete solutionRecall that 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. Now 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 = 223 numerical entries from the file and r = 48 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.(i) Test the claim that p is less than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p < 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301 H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling…
- The profits of a mobile company are normally distributed with Mean of R.O (180) and standard deviatic of R.O (8). a. Find the probability that a randomly selected mobile has a profit greaterthan R.O ( 190). b. Any mobile phone which profit is greater than R.O (190) is defined as expensive. Find the probability that a randomly selected mobile has aprofit greaterthan R.O ( (200) given that it is expensive. Half of expensivemobile phones have aprofit greaterthan R.O h. Find the value of h. C.Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales records, she estimates that P(0)= 0.62, P(1)= 0.21, P(2)= 0.13, P(3)= 0.03, P(4)= 0.01, with negligible probability for higher values of x. Find the long-term average number of homes the real estate agent expects to sell each month.A drawer holds purple socks and yellow socks. If n socks are taken out of the drawer at random, the probability that all are yellow is 1/2. What is the smallest possible number of socks in the drawer (as a function of n)?
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