Answer:
The probability that the wait time is greater than 14 minutes is 0.4786.
Step-by-step explanation:
The random variable X is defined as the waiting time to be seated at a restaurant during the evening.
The average waiting time is, β = 19 minutes.
The random variable X follows an Exponential distribution with parameter [tex]\lambda=\frac{1}{\beta}=\frac{1}{19}[/tex].
The probability distribution function of X is:
[tex]f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...[/tex]
Compute the value of the event (X > 14) as follows:
[tex]P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786[/tex]
Thus, the probability that the wait time is greater than 14 minutes is 0.4786.
