The staff of an organisation are posted in different departments as follows: FIN

Question

The staff of an organisation are posted in different departments as follows: FINANCE 42 male, 28 female- HR 7 male 13 female- OPERATIONS 26 male 9 female. A member of tge staff is selected randomly. Find the probability that a person selected is (1) female (2) female and works in the operations department (3) male or posted in HR department (4) male given that he is not from finance department. The probability distribution of the number of daily successful contracts of a sales representative is as follows: x 0, 1, 2, 3 p(x) 0.25, 0.35, 0.3, 0.1. Calculate the expected number of successful daily contracts per sales representative and its standard deviation. The daily salary (Y) of the sales representative is givenby Y=500+150X. Calculate the expected daily salary and its standard deviation.

Explanation / Answer

n=42+28+7+13+26+9=125

female=50

male=75

1)probability that a person selected is female=50/125=0.4

2.probability that a person selected female and works in the operations department

=76/125

3. probability that a person selected is male or posted in HR department=75/125+20/125

=95/125

4.probability that a person selected male given that he is not from finance department.

=33/125

he probability distribution of the number of daily successful contracts of a sales representative is as follows:

x 0 1 2 3

p(x) 0.25, 0.35, 0.3, 0.1

expected number of successful daily contracts per sales representative

E(X)=sum (0*0.25+1*0.35+2*0.3+3*0.1)

=1.25

standard deviation.

Var=E(X2)-(E(X))2

E(X2)=sum(0*0.25+1*0.35+4*0.3+9*0.1)=2.45

Var=2.45-1.252

=2.45-1.5625

=0.8875

standard deviation.=sqrt(0.8875)

=0.942072

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