Quizzes: Exponential Distribution

by Kurious Fox

Question 1:
The time between arrivals of buses at a bus stop follows an exponential distribution with a mean of 10 minutes. What is the probability that a bus will arrive within the next 5 minutes?

a) 1 - e^{-0.1 \times 5}

b) e^{-0.1 \times 5}

c) 1 - e^{-0.2 \times 5}

d) e^{-0.2 \times 5}

Show answer

1 - e^{-0.1 \times 5}

Question 2:
The time it takes for a taxi to arrive at a taxi stand is exponentially distributed with a rate parameter \lambda = 0.25 per minute. What is the probability that the taxi will take more than 8 minutes to arrive?

a) 1 - e^{-0.25 \times 8}

b) e^{-0.25 \times 8}

c) 1 - e^{-0.125 \times 8}

d) e^{-0.125 \times 8}

Show answer

e^{-0.25 \times 8}

Question 3:
The time between phone calls at a call center is exponentially distributed with an average of 15 minutes. What is the rate parameter \lambda?

a) \frac{1}{30}

b) \frac{1}{15}

c) 15

d) 30

Show answer

\frac{1}{15}

Question 4:
In a theme park, the time between visitors entering the park is exponentially distributed with a mean of 3 minutes. What is the probability that the next visitor will enter within the next 2 minutes?

a) 1 - e^{-3 \times 2}

b) 1 - e^{-\frac{1}{3} \times 2}

c) 1 - e^{-\frac{1}{2} \times 3}

d) e^{-\frac{1}{3} \times 2}

Show answer

b) 1 - e^{-\frac{1}{3} \times 2}

Question 5:
The time until the next financial transaction at a trading desk is exponentially distributed with a mean of 4 minutes. What is the rate parameter \lambda?

a) 0.25

b) 0.5

c) 4

d) 2

Show answer

a) 0.25

Question 6:
The duration of unemployment for workers is exponentially distributed with a rate parameter \lambda = 0.1 per month. What is the probability that a worker will find a job within the next 6 months?

a) e^{-0.1 \times 6}

b) 1 - e^{-0.1 \times 6}

c) e^{-0.6}

d) 1 - e^{-0.6}

Show answer

b) 1 - e^{-0.1 \times 6}


The time between arrivals of buses at a bus stop follows an exponential distribution with a mean of 10 minutes. What is the probability that a bus will arrive within the next 5 minutes?

a) 1 - e^{-0.1 \times 5}

b) e^{-0.1 \times 5}

c) 1 - e^{-0.2 \times 5}

d) e^{-0.2 \times 5}

Show answer

a) 1 - e^{-0.1 \times 5}


The time it takes for a taxi to arrive at a taxi stand is exponentially distributed with a rate parameter \lambda = 0.25 per minute. What is the probability that the taxi will take more than 8 minutes to arrive?

a) 1 - e^{-0.25 \times 8}

b) e^{-0.25 \times 8}

c) 1 - e^{-0.125 \times 8}

d) e^{-0.125 \times 8}

Show answer

b) e^{-0.25 \times 8}

The time between phone calls at a call center is exponentially distributed with an average of 15 minutes. What is the rate parameter \lambda?

a) \frac{1}{30}

b) \frac{1}{15}

c) 15

d) 30

Show answer

b) \frac{1}{15}


In a theme park, the time between visitors entering the park is exponentially distributed with a mean of 3 minutes. What is the probability that the next visitor will enter within the next 2 minutes?

a) 1 - e^{-3 \times 2}

b) 1 - e^{-\frac{1}{3} \times 2}

c) 1 - e^{-\frac{1}{2} \times 3}

d) e^{-\frac{1}{3} \times 2}

Show answer

b) 1 - e^{-\frac{1}{3} \times 2}

The time until the next financial transaction at a trading desk is exponentially distributed with a mean of 4 minutes. What is the rate parameter \lambda?

a) 0.25

b) 0.5

c) 4

d) 2

Show answer

a) 0.25


The duration of unemployment for workers is exponentially distributed with a rate parameter \lambda = 0.1 per month. What is the probability that a worker will find a job within the next 6 months?

a) e^{-0.1 \times 6}

b) 1 - e^{-0.1 \times 6}

c) e^{-0.6}

d) 1 - e^{-0.6}

Show answer

b) 1 - e^{-0.1 \times 6}

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