Question

A doctors office has registered that patients come in independent of each other, that the expected number of patiens per hour is a constant equal to λ = 3, and that there never comes two patients at the same time.

a) What is the probability that there will arrive 10 patients within 3 hours?
b) What is the probability that there will arrive more than 10 patients within 3 hours?
c) What is the expected number of patients within 3 hours?
d) How big is the variance?
e) What is the standard deviation?

Answer 1

X ~ Poi()

Where = 3 per hour.

P(X) = e^- * ^X / X!

a)

For 3 hours, = 3 * 3 = 9

P(X = 10) = e^-9 * 9¹⁰ / 10!

= 0.1186

b)

P(X > 10) = 1 - P(X <= 10)

= 1 - 0.7060 (From cumulative Poisson probability table)

= 0.2940

c)

E(X) = = 9

d)

Variance = = 9

e)

Standard deviation = sqrt () = 3