SOLUTION :
a.
p = f(x)
E(x)
= ∑ f(x) * x
= 0.4*0 + 0.3*1 + 0.2*2 + 0.1*3
= 1.0 company / day (ANSWER).
b.
Variance
= ∑ f(f)( x - E(x))^2
= 0.4(0 - 1)^2 + 0.3(1 - 1)^2 + 0.2(2 - 1)^2 + 0.1(3 - 1)^2
= 0.4 + 0 + 0.2 + 0.4
= 1.0
So,
SD
= sqrt(Variance)
= sqrt(1.0)
= 1.0 company / day (ANSWER).
c.
Company per day = 100/90 = 10/9
P(x > 10/9)
= P(z > (10/9 - 1)/ 1)
= P(z > 0.1111)
From ND table
= 1 - 0.5442
= 0.4558 (ANSWER).
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