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.