Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 0.? computers. i6 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. . What is the distribution or X? X . N( a 5 J, u 7 J) 0' 0' b. What is the distribution of :i'? i . Ni: 4.6 110.1650 \\I] 0' o' c. What is the distribution of Ex? 21 Ntl 52 a J, 2 9698 J; o' o' d. If one randomly selected worker is observed, find the probability that this worker will put together between 4.5 and 4.6 computers per hour. I 0.0565 ~/ 0' e. For the 18 workers, find the probability that their average number of computers put together per hour is between 4.5 and 4.6. 0 2273 I 0' i. Find the probability that a is person shift will put together between 8i and 84.6 computers per hour. in 4555 JJ if g. For part e] and f), is the assumption of normal necessary? C} No@ Yes of\" h. A sticker that says \"Great Dedication" will be given to the groups oi18 workers who have the top 2095 productivity. What is the least total number of computers produced by a group that receives a sticker? _computers per hour (round to the nearest computer) w 9 Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 41 minutes and standard deviation 18 minutes. A researcher observed 41 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( 41 18 b. What is the distribution of E? I ~ N( 41 2.8111 C. What is the distribution of ) ? ) & ~ N( 1681 115.2562 d. If one randomly selected student is timed, find the probability that this student's time will be between 38 and 39 minutes. 0.0219 e. For the 41 students, find the probability that their average time studying is between 38 and 39 minutes. 0.0955 f. Find the probability that the randomly selected 41 students will have a total study time less than 1722 minutes. 0.6390 g. For part e) and f), is the assumption of normal necessary? Yes No h. The top 10% of the total study time for groups of 41 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? 1828.7585 X minutes