Question

Chapter 7 Test Due in 7 hours, 27 minutes. Due Thu 07/30/2020 11:59 pm Questions Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of computers. 11 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. Question 1 (0/10) Question 2 [10/10) Question 3 (0/10) Question 4 [10/101 Question 5 [10/10) Question 6 (0/10) Question 7 [10/10) C Question 8 (0/10) a. What is the distribution of X? X-N b. What is the distribution of i? 2 - N c. What is the distribution of e-n d. If one randomly selected worker is observed, find the probability that this worker will put together between 3.7 and 4.1 computers per hour. For the 1l workers, find the probability that their average number of computers put together per hour is between 3.7 and 4.1. f. Find the probability that all person shift will put together between 42.9 and 47.3 computers per hour. Grade: 40/80 g. For part e) and 1), is the assumption of normal necessary? No Yes h. A sticker that says "Great Dedication" will be given to the groups of 11 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

a)

X ~N(4,1)

b)

std error=σx̅=σ/√n=

0.3015

xbar ~N(4,0.3015)

c)

Σx ~ N(44,3.3166)

d)

probability =P(3.7<X<4.1)=P((3.7-4)/1)<Z<(4.1-4)/1)=P(-0.3<Z<0.1)=0.5398-0.3821=0.1577

e)

probability =P(3.7<X<4.1)=P((3.7-4)/0.302)<Z<(4.1-4)/0.302)=P(-0.99<Z<0.33)=0.6299-0.1599=0.4701

f)

probability =P(42.9<X<47.3)=P((42.9-44)/3.317)<Z<(47.3-44)/3.317)=P(-0.33<Z<0.99)=0.8401-0.3701=0.4701

g) Yes (since n<30)

h)

for 89th percentile critical value of z=1.2265

therefore corresponding value=mean+z*std deviation=48