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:
[tex]P(X=x)=\frac{e^{-7.1}(7.1)^{x}}{x!};x=0,1,2,3...[/tex]
Compute the probability of less than 2 customers arriving as follows:
[tex]P(X<2)=P(X=0)+P(X=1)[/tex]
[tex]=\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[/tex]
Thus, the probability that, in any hour, less than 2 customers will arrive is 0.0067.
