At a local post office, on average, 3 customers are in line when the post office closes

At a local post office, on average, 3 customers are in line when the post office closes each day. The probability, P, that exactly n customers are in line when the post office closes can be modeled by the equation P = (3ⁿe^-3)/n!. Given that e^-3 ≈ 0.05, which of the following values is closest to the probability that exactly 2 customers are in line when the post office closes?

1. 0.08
2. 0.11
3. 0.15
4. 0.23
5. 0.45

Answer

The correct answer is D.

The correct approach for this item is to substitute 2 for n in the formula P = (3ⁿe^-3)/n! and then evaluate. Substituting, we get

P = (3²e^-3)/2!

Now, 3² = 9, 2! = 2, and e⁻³ ≈ 0.05, we get

P ≈ 9(0.05)/2

= 0.225 or 0.23