Answer to Question #238979 in Statistics and Probability for priyanshi

Question

In a given city, 6% of all drivers get at least one parking ticket per year. Use Poisson

approximation to the binomial distribution to determine the probabilities that among

80 drivers, randomly chosen in this city:

a. 4 will get at least one parking ticket in any given year.

Answer 1

Let's find

$\lambda = np = 80 \cdot 0.06 = {\rm{4}}{\rm{.8}}$

Then the wanted probability is

$P(4) = \frac{{{\lambda ^4}}}{{4!}}{e^{ - \lambda }} = \frac{{{{4.8}^4}}}{{24}}{e^{ - 4.8}} \approx 0.182$

Answer: $P(4) \approx 0.182$