Question

A Randstad/Harris interactive survey reported that 25% of employees said their company isloyal to them (USA Today,November 11, 2009). Suppose 10 employees are selected randomlyand will be interviewed about company loyalty.

Round your answers to four decimal places.

a. Is the selection of ten employees a binomial experiment?

Select: Yes/No

Explain.

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b. What is the probability that none of the 10 employees will say their company is loyal to them?

c. What is the probability that four of the 10 employees will say their company is loyal to them?

d. What is the probability that at least two of the 10 employees will say their company is loyal to them?

Answer 1

a. yes

b = 0.0563

c. 0.1460

d. 0.7560

Explanation:

a. Yes. n = 10 identical trials with two possible outcomes on each with p = 0.25.

b. p(x= 0) = 10!/(0!*10!)* .250* .7510= 1 * 1 * 0.0563 = 0.0563.

c. p(x= 4) = 10!/(4!*6!)* .254* .756= 210 * .0039 * 0.1780 = 0.1460

d. p(x= 1) = 10!/(1!*9!)* .251* .759= 10 * .25 * 0.0751 = 0.1877

p(x≥ 2) =1 - p(x< 2) = 1 – (0.0563 + 0.1877) =0 .7560