1t} Treat the number of months X after Januaryr 1 that someone is born as uniformlyr distributed from III to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ [1-, 3.4541 R] b. Suppose that 38 people are surveyed. 1What is the distribution of E for this sample? E ' H[ [a ,05520 l1 a' o' e. What is the probability.r that the average birth month of the 38 people will be less than 6.3? 0.?19 X Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of El? computers. 18 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. a. What is the distribution of X? X N|[I 4. B v'II II]. ? VII} gr\" g' b. What is the distribution of :E? it ~ NI[I 4.6 v" I [II 1650 v'I] bl'i o\" c. What is the distribution of Ex? 23 N {iI 82. 8 'I _l 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. U. (1558 ~/Io' e. For the 18 workers, find the probability that their average number of computers put together per hour is between 4.5 and 4.5. I 112213 I 1'. Find the probability that a 18 person shift will put together between 81 and 84.6 computers per hour. [1.9399 R g. For part e] and f], is the assumption of normal necessary? :31\" h. A sticker that says "Great Dedication" will be given to the groups of18 workers who have the top EOE- 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] CO A computer selects a number A from 2 to 8 randomly and uniformly. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( 2 8 b. Suppose that the computer randomly picks 38 such numbers. What is the distribution of a for this selection of numbers. I ~ N( 5 0.0811 X c. What is the probability that the average of 38 numbers will be less than 5.2? 0.9932 XSuppose 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 N1I:41 I18 x/I} o" 1:1"F b. What is the distribution of 11:? .'i' M4 ,2. 8111 v'I] 1:1\"F :1" c. What is the distribution of 2:11? Z111: N[I 1881 qu I 115. 2582 J} 13" :1" d. If one randomly selected stude_nt' 1s timed, find the probability that this student's time will be between 38 and 39 minutes. _. 823? e. For the 41 students, find the probability that their average time studying is between 38 and 39 minutes. 8.8888 X 1. Find the probability that the randomly selected 41 students will have a total study time less than 1222 minutes. [1.8488 X g. For part e] and f], is the assumption of normal necessary? :1" h. The top 11215-5 of the total study time for groups of 41 studenE 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? 1829 X minutes