English
Menu

Probability, Statistics and Queueing

You arrive at a bus stop served every 10 minutes at a random time, without checking the timetable. The waiting time follows a uniform distribution from 0 to 10 minutes. Which of the following correctly combines the expected waiting time and the probability that the wait is 3 minutes or less?

  1. AExpected value 5 minutes, probability 0.7
  2. BExpected value 10 minutes, probability 0.3
  3. CExpected value 5 minutes, probability 0.3
Show answer and explanation

Answer: C. Expected value 5 minutes, probability 0.3

In a uniform distribution every value in the interval is equally likely, so the expected value is the midpoint of the interval, (0 + 10) ÷ 2 = 5 minutes. The probability that the wait is 3 minutes or less is the fraction of the interval length, 3 ÷ 10 = 0.3.

  • A. 0.7 is the probability that the wait is longer than 3 minutes.
  • B. 10 minutes is the bus interval; the expected waiting time is half of it, 5 minutes.
  • C. Correct. The expected value is 5 minutes, and the probability of waiting 3 minutes or less is 3 ÷ 10 = 0.3.
Practice this topic Back to topic

Related calculators

Queueing calculator (M/M/1 and M/M/c)Utilization, mean waiting time, response time and queue length for M/M/1 and M/M/c from the arrival rate, mean service time and number of servers

Books on Probability, Statistics and Queueing Ad

As an Amazon Associate I earn from qualifying purchases.

More Probability, Statistics and Queueing questions

  1. The dimension of a part follows a normal distribution with a mean of 50.0 mm and a standard deviation of 0.1 mm. Which of the following is closest to the fraction of parts whose dimension lies between 49.7 mm and 50.3 mm?
  2. A scored 80 on test X, and B scored 75 on test Y. Test X had a mean of 65 and a standard deviation of 10, and test Y had a mean of 60 and a standard deviation of 6. Which of the following correctly compares their relative positions within their own tests using the standardized value z = (score − mean) ÷ standard deviation?
  3. The delay of a circuit path varies from chip to chip following a normal distribution with a mean of 940 ps and a standard deviation of 30 ps. Taking the fraction of a normal distribution within the mean ±2σ to be about 95.4%, which of the following is closest to the fraction of chips whose delay exceeds the clock period of 1,000 ps?
  4. The response time of a server was measured 5 times, giving 20, 3, 5, 3 and 4 milliseconds in the order measured. Which of the following is the median of these data?
  5. The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?