BINOMIAL PROBABILITY DISTRIBUTION

AMIN SOKHANVAR

2013-12-20

CREATIVE STYLE AND CUT

• Creative Style and Cut, an upscale beauty salon in San Francisco, offers a full refund to anyone who is not satisfied with the way his or her hair looks after it has been cut and styled. The owners believe the hair style satisfaction from customer to customer is independent and that the probability a customer will ask for a refund is 0.20. Suppose a random sample of six customers is observed. In four instances, the customer has asked for a refund. The owners might be interested in the probability of four refund requests from six customers. If the binomial distribution applies, what is the the probability?

CREATIVE STYLE AND CUT

• Solution:

• Determine the probability of x successes in n trials using the binomial formula. In this case, n 6, p 0.20, q 0.80, and we are interested in the probability of x 4 successes.

• There is only a 0.0154 chance that exactly four customers will want a refund in a sample of six if the chance that any one of the customers will want a refund is 0.20

U.S. BIO

• U.S. Bio, a pharmaceutical company, has developed a drug to restore hair growth in men. Like most drugs, this product has potential side effects. One of these is increased blood pressure. The company is willing to market the drug if there are blood-pressure increases in 2% or fewer of the men using the drug. The company plans to conduct a clinical test with 10 randomly selected men. The number of men with increased blood pressure will be x = 0, 1, 2, . . . 10. find:

• The probability of 2 or fewer men, in a sample of 10, would exhibit increased blood pressure?

• The probability of 3 or more men in the sample of n 10 having high blood pressure as a result of the hair growth drug?

U.S. BIOSolution:

• P(0)= 0.8171

• P(1)= 0.1667

• P(2)= 0.0153

• P(x <2)= P(0)+P(1)+P(2)= 0.9991

NIELSEN TELEVISION RATINGS

• The Nielsen Media Group is the best-known television ratings company. On Tuesday after the 2002 Masters Golf Tournament in Augusta, Georgia, which Tiger Woods won, the company announced that slightly more than 9% of all televisions were tuned to the final round on Sunday. Assuming that the 9% rating is correct, what is the probability that in a random sample of 20 television sets, 2 or fewer would have been tuned to the Masters?

NIELSEN TELEVISION RATINGS

• P(0) = 0.1516

• P(1) = 0.3

• P(2) = 0.2818

• P(x <2)= 0.733