ACNielsen is a New Yorkbased corporation and a member of the

ACNielsen is a New York-based corporation and a member of the modern marketing research industry. One of the hems that ACNielsen tracks is the expenditure on over-the-counter (OTC) cough medicines. ACNielsen recently indie that consumers spent $620 million on OTC medicines in the United States. The article also indicated that nearly 30 million visits for cough made to doctors\' offices in the United States Determine the average cost of OTC cough medicines per doctor\'s office visit based on 30 million purchases. Assuming that the average cost indicated in part a is the true average cost of OTC cough medicines per doctor\' visit and the standard deviation is $10, determine the probability that the average cost for a random selection of 30 individuals will result in an average expenditure of more than $25 in OTC cough medicines. Determine the 90th percentile for the average cost of OTC cough medicines for a sample of 36 individuals, all of whom have visited a doctor\'s office for cough symptoms.

Solution

7.38

a). Average cost = 620/30

= $20.67

b).

standard error for sample of 30 individuals = sd/sqrt(n) = 10/sqrt(30) =1.8257

z value for 25, z=(25-20.67)/1.8257 =2.37

P( x > 25) = p( z >2.37) =0.0089

The required P=0.0089

c).

standard error for sample of 36 individuals = sd/sqrt(n) = 10/sqrt(36) =1.6667

z value for 90^th percentile =1.282

The required x value = mean+z*sd= 20.67+1.282*1.6667 = 22.80671

The required value =$22.81