Using the Poisson distribution, the probabilities are given as follows:
- Less than 6: 0.3837 = 38.37%.
- Exactly 6: 0.1586 = 15.86%.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
The parameters are:
- x is the number of successes
- e = 2.71828 is the Euler number
is the mean in the given interval.
For this problem, the mean is given by:
The probability that exactly 6 tickets are written on a randomly selected day from this population is P(X = 6), hence:
[tex]P(X = 6) = \frac{e^{-6.4}(6.4)^{6}}{(6)!} = 0.1586/tex]
For less than 6, the probability is given by:
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the same formula to find each value and adding them, we have that:
P(X < 6) = 0.3837.
More can be learned about the Poisson distribution at brainly.com/question/13971530
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