Market segmentation is concerned with the recognition of significant differences

Question

Market segmentation is concerned with the recognition of significant differences in buyer characteristics. Generally, the market is partitioned into distinct groups for the purpose of designing products and marketing programs to satisfy the distinctive consumer characteristics of each group. Since the market is often segmented according to the sex of the consumer, a newly designed portable radio was styled by an electronics manufacturer on the assumption that 50% of all purchasers are female. If the manufacturer's assumption is correct and if a random sample of 400 purchasers is selected, what is the probability that the number of female purchasers in the sample will be greater than 175? During periods of economic recession, experience shows that 10% of the people with loans outstanding at a certain commercial bank will become delinquent in their loan repayment schedule. To examine this issue and the characteristics of borrowers from her bank, the bank president randomly selects n = 100 account files at a time in which the economic climate of the community is very uncertain. Find the following probabilities. a. Ten or more of the borrowers are delinquent in their loan repayment schedule. b. No more than 5 are delinquent.

Explanation / Answer

Solution:- The probability that the number of female purchasers in the sample will be greater than 175 is 0.9929.

p = 50/100 = 0.50

n = 400

x = 175

By applying binomial distribution:-

P(x,n,p) = nCx*px*(1 - p)(n - x)

P(x > 175) = 0.9929

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