Question

3. General Hospital has noted that it admits an average of 8 patients per hour.

1. Define the random variable in words for this experiment.

2. What is the probability that during the next hour fewer than 3 patients will be admitted?

3. What is the probability that during the next 2 hours exactly 8 patients will be admitted?

Answer 1

X ~ Poi ( )

Where = 8 per year.

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

a)

P(X < 3) = P(X <= 2)

= P(X = 0) + P(X = 1) + P(X = 2)

= e^-8 + e^-8 * 8 + e^-8 * 8² / 2!

= 0.0138

b)

For 2 hours , = 8 *2 = 16

P( X = 8) = e^-16 * 16⁸ / 8!

= 0.0120