Let X = the Time Between Two Successive Arrivals at the Drive-Up

question 17

Essay

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with $\lambda$ = 1 (which is identical to a standard gamma distribution with $\alpha$ =1), compute the following:
a. The expected time between two successive arrivals.
b. The standard deviation of the time between two successive arrivals.
c. $P ( \bar{X} \leq 5 )$
.
d. $P ( 3 \leq \bar{X} \leq 5 )$
.

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Definitions:

Mind Wandering

The experience of thoughts not remaining on a single topic for a long period, often shifting from one topic to another without any conscious direction.

Consciousness

The state of being aware of and able to think about one’s own existence, sensations, thoughts, surroundings, and experiences.

Somnambulism

Also known as sleepwalking, it is a behavior disorder that originates during deep sleep and results in walking or performing other complex behaviors while asleep.

Excessive Daytime Sleepiness

A condition characterized by persistent sleepiness and often a lack of energy during the day, even after adequate nighttime sleep.