Question

Assume the population of peoples' weights has mean µ = 60 kg. and standard deviation σ = 10 kg. suppose that a small footbridge will break down if the total weight of people on it exceeds 6,200 kg. what is the approximate probability that it will break down if n = 100 people get on it all at once?

a) 0
b) 0.1587
c) 0.0228
d) 0.0013
e) 0.05

Please explain how you got the answer as well please.

Answer 1

Let the total weight of the 100 people be W.
E[W] = 100 * (population mean weight) = 6000 kg
The variance of W will be the sum of the individual variances:
\[\large Var[W]=100\times(10)^{2}=10000\]
Hence the standard deviation of W will be:
\[\large \sqrt{10000}=100\]
Now you can use a standard normal distribution table after finding the z-score for 6200 as follows:
\[\large z=\frac{X-\mu}{\sigma}=\frac{6200-6000}{100}=2\]
The cumulative probability for z >2 can now be found from the table.