Question

Assume that the number of customers who arrive at a water ice stand follows the Poisson distribution with an average rate of 6.4 per 30 minutes. What is the probability that three or four customers will arrive during the next 30 minutes?

Answer 1

Answer:

18.88% probability that three or four customers will arrive during the next 30 minutes

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Average rate of 6.4 per 30 minutes.

This means that $\mu = 6.4$

What is the probability that three or four customers will arrive during the next 30 minutes?

$P = P(X = 3) + P(X = 4)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 3) = \frac{e^{-6.4}*(6.4)^{3}}{(3)!} = 0.0726$

$P(X = 4) = \frac{e^{-6.4}*(6.4)^{4}}{(4)!} = 0.1162$

$P = P(X = 3) + P(X = 4) = 0.0726 + 0.1162 = 0.1888$

18.88% probability that three or four customers will arrive during the next 30 minutes