Answer to Question #343383 in Statistics and Probability for jeff

Question

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

Answer 1

a)

$X\sim Po(\lambda)$

$\lambda=2.2$

$$P(X=0)=\dfrac{e^{-2.2}(2.2)^0}{0!}=0.110803$$

b)

$X\sim Po(\lambda)$

$\lambda=2.2$

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

$$=1-\dfrac{e^{-2.2}(2.2)^0}{0!}-\dfrac{e^{-2.2}(2.2)^1}{1!}$$

$$=0.645430$$

(c) if $n$ is large and $p$ is close to $0,$ the Poisson distribution can be used,

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