A catering company provides packages for weddings and for showers. The cost per person for small groups is approximately Normally distributed for both weddings and showers. The mean cost for weddings is $82.30 with a standard deviation of $18.20, while the mean cost for showers is $65 with a standard deviation of $17.73. If 9 weddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than the mean cost of the showers?