I b The average amount of money spent for lunch per person in the college cafeteria is 56.2 and the standard deviation is $2.01. Suppose that B randomly selected Lunch patrons are observed. Assume the distribution of moneyr spent is normal, and round alL answers to 4 decimal places 1Nhere possible. a. What is the distribution of X? X ~ Nil: II II} I] c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between 35.?98? and 56.1958. | | d. For the group of 8 patrons, find the probability that the average lunch cost is between $5.?98? and 56.1958. | e. For part d}, is the assumption that the distribution is normal necessary? [:3 Test} No b. What is the distribution of o? s ~ N{| I 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. 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. f. g. h. A sticker that says "Great Dedication" will be given to the groups of 18 workers who have the top 2055 . What is the distribution of X? X ~ mi | . What is the distribution of o? o ~ Nii . What is the distribution of 22:? Zn: ~ Nd . 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 I . For the 18 workers, find the probability that their average number of computers put together per hour is between 4.5 and 4.6. i find the probability that a 18 person shift will put together between 81 and 84.6 computers per hour. For part e] and f], is the assumption of normal necessary? [:3 No'C-'Yes productivity. What is the least total number of computers produced by a group that receives a sticker?' lcomputers per hour [round to the nearest computer) 8 A computer selects a number X 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( b. Suppose that the computer randomly picks 38 such numbers. What is the distribution of @ for this selection of numbers. C ~ N( C. What is the probability that the average of 38 numbers will be less than 5.2