Tesla Motors, the automotive company responsible for an array of all-electric au

Question

Tesla Motors, the automotive company responsible for an array of all-electric automobiles such as the Model S, is currently implementing a network of automobile battery charging stations across the United States. Eventually, owners of Tesla automobiles will be able to drive across the entire country, charging their electric cars along the way for free. Statisticians working at headquarters in Palo Alto, CA, have indicated that the distance between charging stations across the country follows an exponential distribution with a mean of 180 miles. (a) If an owner only stops at Tesla charging stations along the way, what is the shortest range a Model S must be able to travel to give the owner an 90% probability of not being stranded due to running out of battery power? (b) The owner of a particular Model S decides to drive from DC to Atlanta. What is the probability that the owner passes at least two charging stations on the 540 mile drive?

Explanation / Answer

Given mean = 180

1/T = 180

a) Given probability of not being stranded due to running out of power = 0.9

1- e^(-xT) = 0.9

0.1 = e^(-x/180)

x = 414.46

b) probability that owner passes atleast two stations on 540 mie drive

p(X>2T)

1- p(X<2T)

= 1 - (1- e^(-2Tx))

= e^(-360/180) = 0.135

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