The magnitude of a load acting on a structure can be modeled

The magnitude of a load acting on a structure can be modeled by a normal distribution with a mean of 100 kips and a standard deviation of 20 kips.

a) If the design load is the 90th percentile value, determine the design load.

b) If the load acting on the structure is 100 kips, what is the probability that the design load will exceed the 90th percentile value?

c) A load with a magnitude less than zero is physically illogical; calculate the probability that the load will be less than zero assuming the normal distribution is somehow an appropriate distribution to model the load.

Solution

a) here for 90th percentile from normal value table ; z =1.2815

hence design load =mean +z*std deviation =125.63

b) probabilty that design load exceed +2 std deviation =P(Z>2) =1-P(Z<2) =1-0.97725 =0.02275

c) probabilty of load less then 0=P(X<0) =P(Z<(0-100)/20) =P(Z<-5)=2.866*10^-7

as probabilty of load less then 0 is approximately 0, but not exactly ), hence in this case it is not appropriate.