Question

A small manufacturing company has 340 employees (excluding top management) classified as supervisors, professional staff, and blue collar workers. It is known that there are 20 supervisors, and 70% of all employees are blue collar workers. Two percent of supervisors, 40% of professional staff, and 74% of blue collar workers are union members. Construct a contingency table given the above data.

a- What percentage of workers are union members?

b- If a random union member employee is selected, what is the probability that he/she is a professional staff?

c- If a random worker is selected, what is the probability that we pick a blue collar union member worker?

d- If a random worker is selected, find the probability of picking a professional staff or non-union employee?

e- Are the classification of workers and their union affiliation independent? Show with calculation.

Answer 1

from given data:

	supervisors	professional staff	blue collar	total
union\	0.4	32.8	176.12	209.32
not union	19.6	49.2	61.88	130.68
total	20	82	238	340

a)

percentage of workers are union members =(209.32/340)*100=61.56

b) probability that he/she is a professional staff =82/340=0.2411

c) probability that we pick a blue collar union member worker =176.12/340=0.5180

d)probability of picking a professional staff or non-union employee =(82+19.6+61.88)/340=0.4808

e)

here P(blue coller)*P(union member)=(238/340)*(209.32)/340)=0.4309 whcihn is not equal to P(blue collar and union member from part C. hence not independent