A small manufacturing company has 340 employees (excluding top management) class

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.

Explanation / Answer

from given data:

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

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

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