Question

Row and Flow is a sports brand that specializes in rowing gear and apparel. They are currently selling two boats:

The King is a high end boat, very high quality and also quite expensive. This boat is a slow moving item, and its monthly demand is estimated to follow a poisson distribution with a lambda of 5. Speedy is a medium quality, more affordable boat. In any given month, the total number of orders for Speedys is uniformly distributed between 5 and 11 (both inclusive).

1) What is the probability that, in any given month, at least one King is sold?

2) What is the probability that, in any given month, the number of Speedys sold is between 5 and 10 (both values inclusive)?

Answer 1

1)

Let Number of King boats sold in a given month be X. The X ~ Poisson( = 5)

probability that, in any given month, at least one King is sold = P(X 1)

= 1 - P(X = 0)

= 1 - e^-5 * 5⁰ /0!

= 1 - e^-5

= 0.9932621

2)

Let Number of Speedys boats sold in a given month be Y. The X ~ Uniform(a = 5, b = 11)

Probability that, in any given month, the number of Speedys sold is between 5 and 10

= P(5 Y 10)

= (10 - 5) / (11 - 5) (For Uniform distribution, P(x1  Y x2) = (x2 - x1) / (b-a) )

= 5/6

= 0.8333333