Question

Poisson Distribution LEARNING OBJECTIVE: Calculate the probability of a poisson distribution. 3.00 The average number of bridge construction projects that take place at any one time in a certain state is 7. PIX=k) - 1e - k is the given number of event occurrences A is the average rate of event occurrences Using the Poisson distribution formula, what is the probability of exactly 4 bridge construction projects taking place at one time in this state? Answer choices are rounded to the hundredths place.

a) 0.09
b) 0.19
c) 0.06
d) 0.05

Answer 1

the required probability is 0.09

Option a) 0.09 is the correct Answer.

Explanation:

Given that;

mean μ = 7

x = 4

the probability of exactly 4 bridge construction projects taking place at one time in this state = ?

Using the Poisson probability formula;

P( X=x ) = ( e^-μ × u^x) / x!

we substitute

P(X = 4) = (e⁻⁷ × 7⁴) / 4!

= 2.1894 / 24

= 0.0875 ≈ 0.09

Therefore the required probability is 0.09

Option a) 0.09 is the correct Answer.