Answer:
Step-by-step explanation
Let β = np, n= 5 and p= 0, 0.1, 0.3, 0.5, 0.9 and 1
x > a, a= 0
The probability of an item inspected, P(x) = β∧x*e∧-β/x!
a) For x= 1: β = 5 X 0 = 0
P(x=1) = 0
For x = 2: β = 5 X 0.1 = 0.5
P(x=2) = 0.5²*e∧-0.5/2!
For x = 3: β = 5 X 0.3 = 1.5
P(x=3) = 1.5³*e∧-1.5/3!
For x =4: β = 5 X 0.5 = 2.5
P(x=4) = 2.5∧4*e∧-2.5/4!
For x = 5: β = 5 X 0.9 = 4.5
P(x=5) = 4.5∧5*e∧-4.5/5!
For x= 6: β = 5 X 1 = 5
P(x= 6) = 5∧6*e∧-5/6!
b) For plan1, x = 1: β + 10 X 0.1 = 1
P(x=1) = e∧-1/1! = 1/e = 1/2.718 = 0.368
For plan2, x=20: β = 100 X 0.1 = 10
P(x=20) = 10∧20*e∧-10/20!
Plan 2 is preferable because the probability of success is very small and the number of trial is comparatively large, hence, the poisson distribution will be suitable probability model.
d) Plan 1 is prefered instead, because the probability of success is larger and more profit is made.
e) Plen 2 is prefered, because it will be cheaper to afford.
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