Market segmentation is concerned with 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 grater than 175?