Question

At the Fidelity Credit Union, a mean of 7.1 customers arrive hourly at the drive-through window. What is the probability that, in any hour, less than 2 customers will arrive

Answer 1

Answer:

The probability that, in any hour, less than 2 customers will arrive is 0.0067.

Step-by-step explanation:

The random variable X can be defined as the number of customers arriving hourly at the drive-through window at the Fidelity Credit Union.

The random variable X describes a finite number of occurrences of an event in a fixed time interval.

The random variable X follows a Poisson distribution with parameter λ = 7.1.

The probability mass function of X is:

$P(X=x)=\frac{e^{-7.1}(7.1)^{x}}{x!};x=0,1,2,3...$

Compute the probability of less than 2 customers arriving as follows:

$P(X$

                $=\frac{e^{-7.1}(7.1)^{0}}{0!}+\frac{e^{-7.1}(7.1)^{1}}{1!}\\\\=0.00083+0.00586\\\\=0.00669\\\\\approx 0.0067$

Thus, the probability that, in any hour, less than 2 customers will arrive is 0.0067.