A survey reported that 35 of employees of company XYZ think

A survey reported that 35% of employees of company XYZ think that the company is loyal to them. Suppose 15 employees are selected randomly and will be interviewed about company loyalty. Is the selection of 15 employees a binomial experiment? Explain. What is the probability that none of the 15 employees will say that the company XYZ is loyal to them? What is the probability that 6 out of 15 employees will say the company is loyal to them? What is the probability that at least 2 out of the 15 employees will say the company is loyal to them?

Solution

There are two outcomes either the employee thinks company is loyal or not loyal

Each employee is independent in his opinion of others.

a) Hence No of employees who feel loyal to the company X (say) out of 15 employees selected is

Binomial with N=15, and p = 0.35

b) Prob that none say xyz is loyal to them

= P(X=0) =(1-0.35)¹⁰

= 0.65¹⁰

= 0.01346

--------------------------

c) Prob that 6 out of 15 employees say company is loyal

= P(X=6)

= 0.1906

d) Prob (atleast 2 loyal)

=P(X>=2)

= 0.9858