According to the central limit theorem, when the sample size is large enough, the distribution of the sample mean that obeys arbitrary distribution approximately obeys normal distribution. Therefore, assuming that each person's weight obeys a normal distribution with a mean value of 60 and a standard deviation of 15, the population of 15 obeys a normal distribution with a mean value of 900 and a standard deviation of sqrt (152 *15) = 54.77.

The condition of overweight is that the total weight in the elevator exceeds 1000 kg, so it is necessary to calculate the probability that the total weight in the elevator exceeds 1000 kg. This probability can be obtained by calculating the cumulative distribution function of standard normal distribution. Let z be a random variable with standard normal distribution, then there are:

z =( 1000-900)/54.77≈ 1.825

The probability of being overweight is:

p(Z & gt； 1.825) ≈ 0.0344

So the probability of being overweight is about 0.0344, which is not equal to the answer given in the question of 0.0426. This result may be caused by the difference between the number of questions and the standard deviation.