Assume that \( A, B, \) and \( C \) are subsets of a sample space \( S \) with \( \Pr(A) = 0.8, \Pr(B) = 0.6, \Pr(C) = 0.15 \).1. Find \( \Pr(A'), \Pr(B'), \) and \( \Pr(C') \). \[ \Pr(A') = \, \text{[ ]} \] \[ \Pr(B') = \, \text{[ ]} \] \[ \Pr(C') = \, \text{[ ]} \]2. If \( \Pr(A \cup B) = 0.85 \), find \( \Pr(A \cap B) \). \[ \Pr(A \cap B) = \, \text{[ ]} \]3. Suppose that we know that \( B \) and \( C \) are disjoint events. Find \( \Pr(B \cup C) \). \[ \Pr(B \cup C) = \, \text{[ ]} \]4. Suppose that instead of being disjoint \( C \subseteq B \). Find \( \Pr(B \cup C) \). \[ \Pr(B \cup C) = \, \text{[ ]} \]

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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15. The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eightfull-time faculty for one week is shown in the table below. At α=0.05, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 11.2 7.5 12.2 7.2 4.1 9.5 13.7 8.5 Question content area bottom Part 1 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ>10.0 Ha: μ≤10.0 B. H0: μ≠10.0 Ha: μ=10.0 C. H0: μ<10.0 Ha: μ≥10.0 D. H0: μ≤10.0 Ha: μ>10.0 E. H0: μ≥10.0 Ha: μ<10.0
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
Suppose a simple random sample of size n = 200 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.8. Complete parts (a) through (c) below. A. Approximately normal Decause ns. and per-p) 1. OB. Not normal because n ≤0.05N and np(1-p) 0.81)? P(p≥ 0.81)= 3632 (Round to four decimal places as needed.) (c) What is the probability of obtaining x= 150 or fewer individuals with the characteristic? That is, what is P(p ≤ 0.75)? P(p ≤ 0.75)= (Round to four decimal places as needed.) + example Get more help. alues % 5 A + 6 MacBook Pro & 7 * 00 8 Vi I, Clear all ( 9 More Check answer X
7. Suppose a teacher looks at a random sample of 42 final exam completion times and finds a mean timeof 111 minutes with asamplestandard deviation of 44 minutes. Which equation should they use tocompute the margin of error?A.E=s√nB.E=z√pqnC.E=zs√nD.E=ts√nE.E=t√pqn 8. Suppose a teacher looks at a random sample of 42 final exam completion times and finds a mean timeof 111 minutes with asamplestandard deviation of 44 minutes. Which value best approximates themargin of error for a 95% confidence interval?A.E= 6.8B.E= 33.4C.E= 13.3D.E= 13.7E.E= 34.4 9. A TWISTER spinner has four outcomes; red, blue, yellow, green. Tim believes that the proportion ofred outcomes is not equal to 25%. Which of the following correctly depicts hisnull hypothesis,H0?A.H0:μ >25B.H0:μ= 25C.H0:μ <25D.H0:μ6= 25E.H0:p=.25F.H0:p > .25G.H0:p < .25H.H0:p6=.25Page 2 10. A TWISTER spinner has four outcomes; red, blue, yellow, green. Tonya tests the claim that theproportion of red…
5. The distribution of male weight in the United States has a standard deviation of roughly o = 25 lbs. The average weight u varies from state to state. Suppose you randomly select 100 males in Louisiana and ask their weights, and you compute the average weight Xn of the n = 100 males. a) Assuming that the standard deviation of weight in Louisiana is 25 lbs, what does the Central Limit Theorem tell you the (approximate) distribution of X will be?
50. Let X₁, X2, ..., X50 be i.i.d. with E(X) = 25 and V(X₂) = 10. Consider the random variable defined by 50 X₁ the sample average X = Σ Apply the Central Limit Theorem to answer the following: n i=1 (a) What is the approximate distribution of X (include parameter(s))? (b) Approximate P(X> 25.5). (c) Approximate P(|X-25 <0.8). (d) Approximate the 0.975 quantile (97.5th%tile) of X.
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