3. Analyzing a binomial experiment using a tree diagram Aa Aa Data from the U.S.

Question

3. Analyzing a binomial experiment using a tree diagram Aa Aa Data from the U.S. Bureau of Labor Statistics show a steady decline in the average workweek of U.S. production workers from 38.5 hours in 1964 to 33.9 hours in 2006. But employees are spending time working when they are at home and behind the wheel. In a poll conducted for Staples, 18% of small-business managers in the United States reported that they read e-mail messages in the bathroom. [Source: Lisa Belkin, "Time Wasted? Perhaps It's Well Spent," The New York Times, May 31, 2007.] Consider the experiment of randomly selecting four small-business managers and learning whether they read e-mail messages in the bathroom. Let R reads e-mail in the bathroom, and Ndoes not read e-mail in the bathroom The experiment satisfies the properties of a binomial experiment. The following tree diagram will help you visualize the sample space for this experiment. First Trial Third Trial Fourth Trial Trial (R, R, R, R) 8 (R, R, R Ny R, R, N, R) 8(R, R, N, NJ (R, N, R, R) 8(R, N, R, N) (R, N, N, R) 82 (R, N, N, N) (N, R, R, R) 8N, R, R, N) (N, R, N, R) 82 (N, R, N, N) .18 .18 .82 .18 18 .18 .18 .18 .18 .18 .18

Explanation / Answer

a)

Of the ___16___ possible experimental outcomes, ___4___ outcomes result in exactly 1 success. [ANSWER]

***********************

b)

Those with one success will have a probability of

0.18*0.82*0.82*0.82 = 0.09924624

= 0.0992 [ANSWER, D]

*********************

C)

Hence, the total probabilty that exactly one manager reads email in the bathroom is

P = 0.09924624*4 = 0.39698496 [ANSWER]

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