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skad [1K]
1 year ago
12

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the

number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day.
Find the probability that less than 6 tickets are written on a randomly selected day from this population. __________

Find the probability that exactly 6 tickets are written on a randomly selected day from this population. ___________
Mathematics
1 answer:
Alexandra [31]1 year ago
4 0

Using the Poisson distribution, the probabilities are given as follows:

  • Less than 6: 0.3837 = 38.37%.
  • Exactly 6: 0.1586 = 15.86%.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}

The parameters are:

  • x is the number of successes
  • e = 2.71828 is the Euler number
  • \mu is the mean in the given interval.

For this problem, the mean is given by:

\mu = 6.4

The probability that exactly 6 tickets are written on a randomly selected day from this population is P(X = 6), hence:

P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}

[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

#SPJ1

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