document.write( "Question 1105395: 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. \n" ); document.write( "

Algebra.Com's Answer #720251 by Boreal(15235) $\"\"$ $\"About$

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The mean of 10 people is 700, since one sums the mean.
\n" ); document.write( "The variance of 10 people is the sum of 10 variances, assuming independence and no covariance.
\n" ); document.write( "sigma ^2=900
\n" ); document.write( "sigma=sqrt (900)=30
\n" ); document.write( "Want to know the probability of finding something in a distribution of N(700, 30) exceeds 800
\n" ); document.write( "z>(800-700)/30=+3.33
\n" ); document.write( "That probability is 0.0004.
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