For per cubic centimeter,
Min. no. of pores, a = 0
mean no. of pores = 20 = (a+b)/2
(a+b)/2 = 20
b = 40
Since uniformly distributed,
probability of each pore, p = 1/40
= 0.025
A.
Let X be the random variable which represents no. of pores per unit volume and is uniformly distributed.
E(X) = 20 (per unit volume)
Expected no. of pores in 0.2cm3 = 20*0.2
= 4
B.
P(X1) = 1-P(x = 0)
= 1-0.025
= 0.975
C.
For 0.2cm3
Expected no. of pores = 4
Min. no. of pores, a = 0
(a+b)/2 = 4
b = 8
probability of each pore, p = 1/8 = 0.125
P(x = 0) = 1/8
= 0.125
i.e 12.5% of the components are going to be produced with zero pores.
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