Individual members of an insured group have independent claims. Aggregate payment amounts for males have mean 2 and variance 4, while payment amounts for females have mean 4 and variance 10. The premium for a group with future claims S is the expected value of S plus 2 times the standard deviation of S. If the genders of the members of a group of m members are not known, the number of males is assumed to have a binomial distribution with mean (0.4)m and variance (0.24)m. Let A be the premium for a group of 100 for which the genders of the members are not known and let B be the premium for a group of 40 males and 60 females. Determine A – B.

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