The magnitude of a load acting in a structure can be modeled by a normal distrib
ID: 3205312 • Letter: T
Question
The magnitude of a load acting in a structure can be modeled by a normal distribution with a mean of 100 kip and a standard deviation of 20kip.
(a) If the design load is considered to be the 90th percentile value, determine the design load.
(b) If the design load is considered to be the mean +2 standard deviation value, what is the probability that it will be exceeded?
(c) A load of magnitude less than zero is physically illogical; calculate its probability. Is a normal distribution appropriate to model the load?
Explanation / Answer
Mean ( u ) =100
Standard Deviation ( sd )=20
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P ( Z < x ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is 1.282
P( x-u/s.d < x - 100/20 ) = 0.9
That is, ( x - 100/20 ) = 1.28
--> x = 1.28 * 20 + 100 = 125.64
b.
from the empirical rule
About 95% of the area under the normal curve is within two standard deviation of the mean. i.e. (u ± 2s.d)
So to the given normal distribution about 95% of the observations lie in between
= [500 ± 2 * 10]
= [ 500 - 2 * 10 , 500 + 2* 10]
= [ 480 , 520 ]
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