1. The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. a. What is the probability that you wait longer than one hour for a taxi

The answer is below

Step-by-step explanation:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is the probability that you wait longer than one hour for a taxi? (b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes? (c) Determine x such that the probability that you wait more than x minutes is 0.10. (d) Determine x such that the probability that you wait less than x minutes is 0.90.

A continuous variable is has a probability distribution function as:

A continuous variable is has a cumulative distribution function as:

Given mean  = 10 minutes

a) P(X > 1 hour) = P(X > 60 minutes) = 1 - F(60) =

b) P(X < 70 | x > 60) = P(X < 10) =

c) 0.1 = P(X > x)

0.1 = 1 - F(x)

d) 0.9 = P(X < x)

0.9 = F(x)