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2. The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the results shown in the table below. Complete (a) and (b) to the right. Arrivals Frequency CJ 0 12 29 2 49 3 41 4 31 5 22 6 10 7 5 8 a. Compute the expected number of arrivals per minute. µ = □ (Type an integer or decimal rounded to three decimal places as needed.) b. Compute the standard deviation. cr = (Type an integer or decimal rounded to three decimal places as needed.) -, .:l. 4. If n = 6 and 1t = 0.45, what is the probability of the following? a. X=5 b. X:o::;4 c. X<3 d. X>2 a. P(X = 5) = lJ (Round to four decimal places as needed.) b. P(X::;; 4) = D (Round to four decimal places as needed.) c. P(X < 3) = D (Round to four decimal places as needed.) d. P(X > 2) = D (Round to four decimal places as needed.) A student is taking a multiple-choice exam in which each question has five choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place five balls (marked A, B, C, D, and E) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are four multiple-choice questions on the exam. Complete parts (a) through (d) below. a. What is the probability that she will get four questions correct? D (Round to four decimal places as needed.) b. What is the probability that she will get at least three questions correct? LJ (Round to four decimal places as needed.) c. What is the probability that she will get no questions correct? ,........, L___l (Round to four decimal places as needed.) d. What is the probability that she will get no more than two questions correct? D (Round to four decimal places as needed.) 5. Last year, a survey was conducted on adults living in a certain country. When asked about the current state of the job market, 55% indicated that now is a good time to be looking for a quality job. The remainder answered no opinion or that now is a bad time to be looking for a quality job. Suppose that you select a random sample of 10 adults and survey them concerning the current state of the job market. Assume that 55% of the adults in that country still think that now is a "good time" to be looking for a quality job, and further assume that the number of the 10 adults thinking that now is a "good time" is distributed as a binomial random variable. Complete parts (a) through (d) below. a. What are the mean and standard deviation of this distribution? The mean isO adults. (Type an integer or a decimal.) The standard deviation is O adults. (Round to three decimal places as needed.) b. What is the probability that exactly two think that now is a "good time"? LJ (Round to four decimal places as needed.) c. What is the probability that two or less think that now is a "good time"? D (Round to four decimal places as needed.) d. If two adults in your survey indicate that now is a "good time," do you think that 55% of the adults in that country still think that now is a good time to look for a quality job? QA. Yes, because the percentage of adults in your survey that think that now is a "good time" is approximately 55%. C)B. No, because the percentage of adults in your survey that think that now is a "good time" is greater than 55%. QC. No, because the percentage of adults in your survey that think that now is a "good time" is less than 55%. 6. 7. Assume a Poisson distribution. a. If;\,= 2.5, find P(X = 6). c. If;\,= 0.5, find P(X = 2). a. P(X=6)= □ (Round to four decimal places as needed.) b. P(X= I)= □ (Round to four decimal places as needed.) c. P(X= 2)= □ (Round to four decimal places as needed.) d. P(X=9)= □ (Round to four decimal places as needed.) b. If;\,= 8.0, find P(X = I). d. If;\,= 3.7, find P(X = 9). Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 1.9. Complete parts (a) through (d}. a. What is the probability that in any given day zero network errors will occur? The probability that zero network errors will occur is 0- (Round to four decimal places as needed.) b. What is the probability that in any given day exactly one network error will occur? The probability that exactly one network error will occur is D- (Round to four decimal places as needed.) c. What is the probability that in any given day two or more network errors will occur? The probability that two or more network errors will occur is O. (Round to four decimal places as needed.) d. What is the probability that in any given day less than three network errors will occur? The probability that less than three network errors will occur is D- (Round to four decimal places as needed.) 8. The quality control manager of Marilyn's Cookies .is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.1. Complete parts (a) through (d). a. What is the probability that in any particular cookie being inspected less than five chip parts will be found? The probability that any particular cookie has less than five chip parts is □. (Round to four decimal places as needed.) b. What is the probability that in any particular cookie being inspected exactly five chip parts will be found? The probability that any particular cookie has exactly five chip parts is D­ (Round to four decimal places as needed.) c. What is the probability that in any particular cookie being inspected five or more chip parts will be found? The probability that any particular cookie has five or more chip parts is (Round to four decimal places as needed.) d. What is the probability that in any particular cookie being inspected either four or five chip pa1ts will be found? The probability that any particular cookie has four or five chip parts is D­ (Round to four decimal places as needed.) 9. One year, an airline had 6.98 mishandled bags per 1,000 passengers. Complete parts (a) through (c). a. What is the probability that in the next 1,000 passengers, the airline will have no mishandled bags? The probability that the airline will have no mishandled bags is D­ (Round to four decimal places as needed.) b. What is the probability that in the next 1,000 passengers, the airline will have at least one mishandled bag? The probability that the airline will have at least one mishandled bag is LJ. (Round to four decimal places as needed.) c. What is the probability that in the next 1,000 passengers, the airline will have at least two mishandled bags? The probability that the airline will have at least two mishandled bags is D­ (Round to four decimal places as needed.)

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