11. 12. 13. 14. 15. ([4]. m 3i] The IT department at a company purchases top of the line laptops and buys them in lots of size 10' It is their policy to inspect 3 laptops randomly from a lot and to accept the lot if all 3 are nondefective. If 30% of the lots have 4 defective laptops and 70% have only 1, what proportion of lots does the IT department reject? ([6], 4.51 ) Working as a research assistant over the summer, you and your fellow ctrworkers produce a large amount of Dede over 4 months .Throughout this time ,data has been collected to review the amount of errors , X, per every 100 lines of code , and the following probability distribution was determined: Find the mean and variance of the discrete random variable Z = 3X 2, when X represents the number of errors per 100 lines of code ([5]: 5-5) According to a survey by the Administrative Management Society, oneihalf of U.S. companies give employees 4 weeks of vacation after they have been with the company for 1.5 years. Find the probability that among 6 companies surveyed at random, the number that give employees 4 weeks of vacation after 15 years of employment is a] Anywhere from 2 to 5. b) Fewer than 3. [[6], 5.57 ) The probability that a student passes their designation exam after graduation is 0.7 . Find the probability that the student will pass the exam 3) 0n the third try. b) Before the fourth try. ([6], 5.1 and 5.3) An employee is selected from a staff of ll] to supervise a certain project by selecting a tag at random from a box containing 10 tags numbered From 1 to 10. a} Find the formula for the probability distribution of X representing the number on the tag that is drawn. What is the probability that the number drawn is less than 4? h) Find the mean and variance of the random variable. ([5]: 5-79 l The length of time between breakdowns of an essential piece of equipment in an office is important in the decision of the use of the equipment . Suppose that the best 'model ' for time between breakdowns of the equipment is the exponential distribution, with a mean of 15 days a) If the equipment has just broken down, what is the probability that it will break