Question

A bridge crossing a river can support at most 85,000 lbs. Suppose that the weights of automobiles using the bridge have mean weight 3,200 lbs and standard deviation 400 lbs. How many automobiles can use the bridge simultaneously so that the probability that the bridge is not damaged is at least 0.99?

Answer 1

let

X is the weight of automobiles

so X~(mean=3200, Sd=400)

let the required number of automobiles is "n"

then

we have to find the "n" for

P(S<85000)=0.99

now

from

Z table

P(Z<2.326)=0.99

this gives

solving it

so

n~ 25