# Question: Lights used to illuminate a long stretch of Highway 46

Lights used to illuminate a long stretch of Highway 46 burn out at an average rate of 2.3 per day. (Assume that all the Poisson conditions are met.) Letting x represent values of the random variable “number of lights that burn out during any one day,” use the Poisson table to

a. Determine the probability that x = 2 (that is, the probability that exactly 2 lights will burn out on a randomly selected day).

b. Compute the expected number of lights that will burn out on a given day as

E(x) = ∑[x. P(x)].

c. Compare your answer in part b to the value of λ.

d. Compute the variance for the distribution using the general expression

σ2 = ∑[(x ─ E(x))2 • P(x)].

e. Compare your answer in part d to the value of λ.

a. Determine the probability that x = 2 (that is, the probability that exactly 2 lights will burn out on a randomly selected day).

b. Compute the expected number of lights that will burn out on a given day as

E(x) = ∑[x. P(x)].

c. Compare your answer in part b to the value of λ.

d. Compute the variance for the distribution using the general expression

σ2 = ∑[(x ─ E(x))2 • P(x)].

e. Compare your answer in part d to the value of λ.

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