Answer to Question #343383 in Statistics and Probability for jeff

Question #343383

Suppose that the average number of cars abandoned weekly on a certain highway is2.2.


Approximate the probability that there will be:


(a) no abandoned cars in the next week;


(b) at least 2 abandoned cars in the next week. . . " .....


(c) State the key assumptions needed to' make your answers in a) and b) reasonable

1
Expert's answer
2022-05-23T22:54:13-0400

a)

XPo(λ)X\sim Po(\lambda)

λ=2.2\lambda=2.2


P(X=0)=e2.2(2.2)00!=0.110803P(X=0)=\dfrac{e^{-2.2}(2.2)^0}{0!}=0.110803

b)

XPo(λ)X\sim Po(\lambda)

λ=2.2\lambda=2.2


P(X2)=1P(X=0)P(X=1)P(X\ge 2)=1-P(X=0)-P(X=1)

=1e2.2(2.2)00!e2.2(2.2)11!=1-\dfrac{e^{-2.2}(2.2)^0}{0!}-\dfrac{e^{-2.2}(2.2)^1}{1!}

=0.645430=0.645430



(c) if nn is large and pp is close to 0,0, the Poisson distribution can be used,

with μ=np,μ = np, to approximate binomial probabilities.



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