Question;Chap 4: 8, 12, 20, 26, 30, 38, 44, 62, 68, 74 4-8 The results of a census of 2500 employees of a mid-size company with 401k retirement accounts are as follows: Acount balance Male Female Total 100,000 155 45 200 Total 1490 1010 2500 Suppose researchers are going to sample employees from the company for further study. a Based on the relative frequency assessment method, what is the probability that a randomly selected employee will be a female? b Based on the relative frequency assessment method, what is the probability that a radomly selected employee will have a 401(k) account balance between $25,000 and $49,000? c Compute the probability that a randomly selected employee will be female with an account balance between $50,000 and $99,999. 4-12 Cyber Communications Inc has a new cell phone product under development in the research and development (R&D) lab. It will increase the megapixel capability of cell phone cameras to the 6+ range. The head of R&D made a presentation to the company CEO stating that the probability will earn a profit in excess of $20 million next year is 80%. Comment on this probability assessment. 4-20 VERCOR provides merger and acquisition consultants to assist corporations when an owner deciders to offer the business for sale. One of their new releases, "Tax Audit Frequency is Rising" written by David L Perkins Jr., a VERCOR partner, orginally appeared in The Business Owner. Perkins indicated that audits of the largest businesses, those corporations with assets of $10 million and over climbed to 9,560 in the previous year. That was up from a low of 7,125 a year earlier. He indicated one in six large corporations being audited. a Designate the type of probability assessment method that perkins used to asses the probability of large corporations being audited. b Determine the number of large corporations that filed tax returns for the previous fiscal year. c Determine the probability that a large corporation was not audited using the relative frequency probability assessment method. 4-26 Based on whether data collected in Rachine, Wisconsin, on Christmas day, the weather had the following distribution. Event Relative Frequency Clear & dry 0.2 Cloudy & dry 0.3 Rain 0.4 Snow 0.1 a Based on these data, what is the probability that next christmas will be dry? b Based on the data, what is the probability that next Christmas will be raining, or cloudy, or dry? c Supposing next christmas is dry, determind the probability that it will also be cloudy? 4-30 Micron Technology has sales offices located in four cities: Dallas, Seattle, Boston, and Los Angeles. An analysis of the company's accounts receivables reveals the number of overdue invoices by days, as shown here. Days overdue Dallas Seattle Boston Los Angeles Total Under 30 days 137 122 198 287 744 30-60 days 85 46 76 109 316 61-90 days 33 27 55 48 163 Over 90 days 18 32 45 66 161 Total 273 227 374 510 1384 a What is the probability that a randomly selected invoice from the database is from the Boston sales office. b What is the probability that a randomly selected invoice from the database is between 30 and 90 days overdue? c What is the probability that a randomly selected invoice from the database is over 90 days old and from the Seattle office? d If a randomly selected invoice is from the Los Angeles office, what is the probability that it is 60 or fewer days overdue? 4-38 The snappy Service gas station manager is thinking about a promotion that she hopes will bring in morebusiness to the full-service island. She is considering the option that when a customer requests a fill-up, if the pump stops with the dollar amount $19.99, the customer will get free gasoline. Previous studies show that 70% of the customers require more than $20.00 when they fill up, so would not be eligible for the free gas. What is the probability that a customer will get free gas at this gas station if the promotion is implemented? 4-62 Examine the relationship between independednt, dependent, and mutally exclusive events. Consider two events A and B that are mutally exclusive such that P(A) DOES NOT EQUAL 0. b What does your answer to part A say about whether two mutually exclusive events are dependent or independent? Given that P (A) does not equal to 0 and we obtain P (A|B) = 0. Since P(A) is not equal to P (A|B), events A and B are dependent. Therefore, two mutually exclusive events are always dependent. c Consider these two events C and D such that P(C) =.4 AND P(C|D) = 0.15. (1) Are events C and D mutually exclusive? (2) Are events C and D independent or dependent? Are dependent events necessarily mutually exclusive events? 4-68 Simmons furniture company is considering changing its starting hour from 8:00AM to 7:30AM. A census of the company's 1200 office and production workers shows that 370 of its 750 product workers favor the change and a total of 715 workers favor the change. To futher assess worker opinion, the region manager decides to talk with random workers. Opinion on Change Product Office Totala What is the probability a randomly selected worker will be in favor of the change. Favor 370 345 715b What is the probability a randomly selected worked will be against the change and be an office worker? c Are the events job type and opinion independent? Explain. 4-74 A manufacturing firm has two suppliers for an electrical component used in its process: one in Mexico and one in China. The supplier in Mexico ships 82% of all the electrical components used by the firm and has a defect rate of 4%. The chinese supplier ships 18% of teh electrical components used by the firm and has a defect rate of 6%. a Calculate the probabiltiy that an electrical component is defective? b Suppose an electrical component is defective. What is the probability that component was shipped from Mexico? (Hint use Bayes theorem).
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