What is the standard deviation? A large multinational firm determined that its e

Question

What is the standard deviation? A large multinational firm determined that its employees were rated on performance as follows: 10% were outstanding: 75% were excellent/good; 10% were satisfactory; and 5% were unsatisfactory. Use these ratings to answer answer questions about a sample of 10 employees, selected at random. What is the probability that 1 employee will be rated outstanding? What is the probability that 3 or fewer employees will be rated as satisfactory? What is the probability that exactly 4 employees will be rated excellent/Good? What is the probability that at least 2 employees will be rated as unsatisfactory

Explanation / Answer

a.The probability that 1 employee will be rated outstanding is:

10C1*0.10^1*0.90^9

=10!/9!*1!*0.10*0.90^9

=0.387

b.The probability that 3 or fewer is satisfactory:

P(X<=3)

=P(X=0)+P(X=1)+…+P(X=3)

=10C0*0.10^0*0.90^10+…+10C3*0.10^3*0.90^7

=0.987

C.The probability that exactly 4 are excellent:

10C4*0.75^4*0.25^6

=10!/4!*6!*0.75^4*0.25^6

=0.016

d.The probability that at least 2 are unsatisfactory:

P(X>=2)

=10C2*0.05^2*(1-0.05)^8+…+10C10*0.05^2*(1-0.05)^10

=0.086

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