Showing 11 to 20 of 2584 Questions

(From vos Savant26) A reader of Marilyn vos Savant’s column wrote in with the following question:My dad heard this story on the radio. At Duke University, two students had received A’s in chemistry all semester. But on the night before the final exam, they were partying in another state and didn’t get back to Duke until it was over.
0359 
(Johnsonbough8) A coin with probability p for heads is tossed n times. Let E be the event “a head is obtained on the first toss and Fk the event ‘exactly k heads are obtained.” For which pairs (n, k) are E and Fk independent?
0358 
1. A Poisson model is well suited to this application so long as the defects come in small clusters of two or three together. 2. To use a Poisson model for the number of defects, we must assume that defects occur at an increasing rate throughout the manufacturing of the fabric. 3. An increase in the amount of fabric from 2 to 4 square yar
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1. Expression for the variance of Y 2. Probability that the first trial B1 fails. 3. Expression for the mean of X 4. Probability that Y is zero 5. Probability that X is 2 6. Covariance between B1 and B2 7. Expression for the expected value of Y 8. The expected value of B1 9. Probability that Y is n 10. Probability that X is zero (a) np (b
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1. If A1 is independent of A2, P (A)  A2) = P (A2). Exercises 15–20. The Human Resources division classifies employees of the firm into one of three categories: administrative, clerical, or management. Suppose we choose an employee at random. Define the events A = {administrative}, C = {clerical}, M = {management} Event A occurs, for e
01 
1. If the graduate applies to all 10 companies, what is the probability that she will get at least one offer? 2. If she can apply to only one company, based on cost and success probability criteria alone, should she apply to company 5? Why or why not? 3. If she applies to companies 2, 5, 8, and 9, what is the total cost? What is the proba
012 
1. If the selected 25 transactions are treated as Bernoulli trials, the resulting binomial calculations will be in error because of sampling from a finite population. 2. The binomial model for this problem sets n = 25 and p = 0.10. 3. Assuming Bernoulli trials, there is a 1>1,000 chance for at least one error among the first three transac
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1. Independent events 2. Disjoint events 3. Union 4. Intersection 5. Complement of A 6. Sample space 7. Addition Rule 8. Complement Rule 9. Boole’s inequality 10. Dependent events (a) P (A and B) = P (A) × P(B) (b) Ac (c) S (d) P (A or B) + P (A and B) = P (A) + P(B) (e) P (A or B) … P (A) + P (B) (f) A and B (g) P (A and B) = 0 (h)
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1. Mean of X 2. Variance of X 3. Probability of X being less than its mean 4. Probability of X being less than μ + σ 5. Standard deviation of Z 6. Probability that a zscore based on X is less than 1 in magnitude 7. Proportion of a normal distribution that is more than 20 σ from m 8. Difference between value of P(Z < – x) and value o
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1. More employees at the processing center are older than 44 than between 38 and 44. 2. Most of the employees at this center are older than 25. 3. If the company were to convert these ages from years to days, then the ages in days would also be normally distributed. 4. If none of these employees leaves the firm and no new hires are made,
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