Question

A. what is the probability that a service time is less than or equal to one minute (to 4 decimals)?

Answer 1

The complete question says:
"Wendy's restaurant has been recognized for having the fastest average service time among fast food restaurants. In a benchmark study, Wendy's average service time of 2.2 minutes was less than those of Burger King, Chick-fil-A, Krystal, McDonald's, Taco Bell, and Taco John's (QSR Magazine website, December 2014). Assume that the service time for Wendy's has an exponential distribution.

a. What is the probability that a service time is less than or equal to one minute (to 4 decimals)?"

The exponential distribution probability is given by the formula:

$P(T \leq t) = 1 - e^{-\lambda t}$

where: 

λ = average in unit time = 1/2.2 = 0.45 services per minute       

t = time requested = 1 minute

$P(T \leq 1) = 1 - e^{-0.45}$

p(T ≤ 1) = 0.3624

Hence, the probability that a service time is less than or equal to one minute is p = 0.3624, which means 36.24%.