2. According to company records, 5% of all automobiles brought to Geoff’s Garage last year for a state-mandated annual inspection did not pass. Of the next 10 automobiles entering the inspection station,
what is the probability that none will pass inspection?
what is the probability that all will pass inspection?
what is the probability that exactly 2 will not pass inspection?
what is the probability that more than 3 will not pass inspection?
what is the probability that fewer than 2 will not pass inspection?
Find the expected number of automobiles not passing inspection.
Determine the standard deviation for the number of cars not passing inspection.
here this is binomial with parameter n=10 and p=0.05 |
a)
probability = | P(X=10)= | (_{n}C_{x})p^{x}(1−p)^{(n-x) } = 0.05^{10} = | 0.0000 |
b)
e probability that all will pass inspection:
probability = | P(X=0)= | (_{n}C_{x})p^{x}(1−p)^{(n-x) } = 0.95^{10} = | 0.5987 |
c)
probability = | P(X=2)= | (_{n}C_{x})p^{x}(1−p)^{(n-x) } = | 0.0746 |
d)
probability = | P(X>3)= | 1-P(X<=3)= | 1-∑_{x=0}^{3} (_{n}C_{x})p^{x}(1−p)^{(n-x) } = | 0.0010 |
e)
probability = | P(X<1)= | ∑_{x=0}^{x } (_{n}C_{x})p^{x}(1−p)^{(n-x) } = | 0.9139 |
f)
mean of distribution=expected number μ=np= | 0.50 |
g)
standard deviation σ=√(np(1-p))= | 0.6892 |
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