The average number of bridge construction projects that take place at any one time in a certain state is 7.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.
Question
The average number of bridge construction projects that take place at any one time in a certain state is 7.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.
Solution
To solve this problem, we will use the Poisson distribution formula, which is:
P(x; μ) = (e^-μ) * (μ^x) / x!
Where:
- P(x; μ) is the probability of x events happening in an interval,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average rate of value (in this case, 7 bridge construction projects),
- x is the actual number of successes that result from the experiment (in this case, 4 bridge construction projects).
Substituting the given values into the formula, we get:
P(4; 7) = (e^-7) * (7^4) / 4!
Calculating the above expression will give us the probability of exactly 4 bridge construction projects taking place at one time in this state.
Let's calculate it:
P(4; 7) = (0.000911881) * (2401) / 24 P(4; 7) = 0.090223522
So, the probability of exactly 4 bridge construction projects taking place at one time in this state is approximately 0.09 or 9% when rounded to the hundredths place.
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