Question

7) Based on past records, the average number of two-car accidents in a New York City police precinct is 10.1 per day. What is the probability that there will be: a) at least fourteen such accidents on any given day? b) not more than seven such accidents on any given day? c) at least seven but not more than twelve such accidents on any given day? d) fewer than ten such accidents on any given day?

Answer 1

6)
lambda = 10.1

As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

a)
P(X >=14) = 1 - P(X < 14) = 0.1429

b)
P(X <= 7) = 0.2113

c)
P(7<= X <= 12) = 0.658

d)
P(X < 10) = 0.4455