SOLUTION: The elevator installed in a building can carry up to 10 people or a maximum weight of 800 kg. It is known that the weight of the people in this building follows a normal distributi

Question 1105421: The elevator installed in a building can carry up to 10 people or a maximum weight of 800 kg. It is known that the weight of the people in this building follows a normal distribution with mean μ= 70 and variance σ^2 = 90. Calculate the probability that the sum of the weights of 10 persons together in the elevator exceeds the maximum weight.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The mean of 10 people is 700, since one sums the mean.
The variance of 10 people is the sum of 10 variances, assuming independence and no covariance.
sigma ^2=900
sigma=sqrt (900)=30
Want to know the probability of finding something in a distribution of N(700, 30) exceeds 800
z>(800-700)/30=+3.33
That probability is 0.0004.
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