A variable follows the triangular distribution and has a lower limit of 200, an upper limit of 1600, and the most likely value of 750. Find the following:
a)Value of Standard Deviation
b)Probability the variable is less than 600?
c)Probability that variable is greater than 1000?
d)Probability the variable is between 800 and 1000?
for triangular distribution
a= | 200 |
b= | 1600 |
m = | 750 |
a)
V(X)=(1/18)*(a2+b2+m2-ab-am-bm)= | 82916.667 | ||
standard deviation =σ = | 287.953 |
b)
Probability the variable is less than 600
P(X<600 ) =(x-a)2/((b-a)*(m-a)) =(600-200)^2/((1600-200)*(750-200))= | 0.2078 |
c)
for 1000 >750:
Probability that variable is greater than 1000 :
P(X>1000)=(b-x)2/((b-a)*(b-m))=(1600-1000)^2/((1600-200)*(1600-750)) | =0.3025 |
d)
Probability the variable is between 800 and 1000 :
P(800 <X<1000) =P(X<1000)-P(X<800)
=(1600-800)^2/((1600-200)*(1600-750))-(1600-1000)^2/((1600-200)*(1600-750))
=0.2353
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