Question

Each sweat shop worker at a computer factory can put together 4.6 computers per hour on average with a standard deviation of 1 computers. 41 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-NC 0,1 b. What is the distribution of a? -NE c. What is the distribution of 2 --N 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. e. For the 41 workers, find the probability that their average number of computers put together per hour is between 4.5 and 4.6. f. Find the probability that a 41 person shift will put together between 180.4 and 184.5 computers per hour. g. For part e) and f), is the assumption of normal necessary? No Yes h. A sticker that says "Great Dedication" will be given to the groups of 41 workers who have the top 10% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

Answer 1

Answerin * Here we have to find the a-score then find the probability foam standard normal distribution. a) Distribution of x Xro normal (H=4.6, 0:1) b) Distribution of X & normal (N=4.6, Jaw). ie. y no normal (M=4.6 ก -0.1561744) c) Distribution of [x; Exin normal (n=41846, 500=541x1) =x; 1 SUỐTa (nu - 1 88-6 , J6-- 6.403124) d) PC 4.5<x<416) 4.6-4*6 OP 45-4-6 L P (45-4-6 let PC-0.1<Zc co PEZ CO] - P[2C-0.1] 0.5-0.4601722 0.0348278 = 0.03983

6-4.6 7 2 usul f) PC180.42 EX: 2184.5) e) PC 4.5 < X 44-6) =P 4-5 XM 4.6-4.6 olun Your P[-0.64 Le co] P[zco) - PCZC-0.64] 0.5-0.2610863 : 0.238914. = Ć P I gotta 180.4-188.6 184-5-188.6 < za 6.403124 6.403124 - P[-1.28 LZc10.64) 7 DEZO:64 EPCZ2-0.64] - P(ZC-1.28) - 0.2610863-0.1002726 0.1608137 g) for e) 8F) assumption of normal necessary > yes Because if x is non-nornal then ☆ ☆ Ey; cannot be normal.

h ) P(x2) : .. 1- P(८) -0.1 PCxex) - ०.१ (" from z Inverse table) P(२८1.285):०.१ > x - 188.6 - 1285 6.403124 x188.6 - 8.228 ४- 8228 + 1886 x = 1१6.828 x - १ ७ 1१२ The least total