The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.44. Please give your answers to two decimal places. What is the probability that the time between consecutive customers is less than 15 seconds?

Answer:0.4327Step-by-step explanation:Mean = [tex]\mu = 0.44[/tex]We are supposed to find the probability that the time between consecutive customers is less than 15 seconds[tex]\mu = \frac{1}{\lambda}[/tex][tex]0.44 min = \frac{1}{\lambda}[/tex][tex]0.44 \times 60 = \frac{1}{\lambda}[/tex][tex]\lambda = \frac{1}{0.44 \times 60}[/tex][tex]\lambda = 0.0378[/tex]The cumulative distribution function : [tex]P(X \leq x)=F(x)=1-e^{-\lambda x}[/tex]We are supposed to find the probability that the time between consecutive customers is less than 15 seconds[tex]P(X \leq 15)=F(15)=1-e^{-0.0378 \times 15}[/tex][tex]P(X \leq 15)=F(15)=0.4327[/tex]Hence the probability that the time between consecutive customers is less than 15 seconds is 0.4327