Copyright

Calculating the Variance of a Poisson Distribution

  • 1.

    On average 15 people arrive at the park per hour. If x represents the number of people, then what is the variance for x assuming we are looking between 8:00 am and 9:00 am?

    Answers:

    • {eq}(15)^{1/2} {/eq}

    • {eq}15^2 {/eq}

    • {eq}15 {/eq}

    • {eq}\dfrac{15}{2} {/eq}

  • 2.

    A bank server can serve 3 customers per minute. If it follows the Poisson distribution, then what is the variance for the number of customers in 30 minutes?

    Answers:

    • {eq}30 {/eq}

    • {eq}3 {/eq}

    • {eq}3 \times 30 {/eq}

    • {eq}3^{30} {/eq}

  • 3.

    The arrival of trains follows a Poisson process that has a rate of arrival of 3 per hour. Calculate the variance of the arrival of trains in two hours.

    Answers:

    • 3

    • 9

    • 1.5

    • 6

  • 4.

    A discrete variable x follows a Poisson distribution with a rate parameter of 22. Find the variance of x for time 1.

    Answers:

    • {eq}22 {/eq}

    • {eq}22^{1/2} {/eq}

    • {eq}11 {/eq}

    • {eq}22^2 {/eq}

  • 5.

    The number of bookings for a movie can be modeled using a Poisson process with 100 bookings in 30 minutes. Find the variance for the number of bookings in an hour.

    Answers:

    • 300

    • 50

    • 100

    • 200

  • 6.

    On average, there are 5 typos per 50 pages in a book. There are 500 pages in that book. Find the variance for the number of typos in the entire book.

    Answers:

    • 5x500

    • 50

    • 5

    • 500

  • 7.

    Assuming that the number of bikes passing a red light can be modeled using a Poisson distribution with a mean of 15 per minute, calculate the variance for the number of bikes between 11 am and 12 pm.

    Answers:

    • 900

    • 150

    • 90

    • 1500

  • 8.

    The arrival of a bus at the bus stand follows a Poisson distribution with the rate of 3 per hour. What is the variance for the number of buses arriving in 3 hours?

    Answers:

    • 9

    • 27

    • 12

    • 3

  • 9.

    For a Poisson process, {eq}\lambda = 2 {/eq}. What is the value of the variance, {eq}V(X) {/eq}?

    Answers:

    • {eq}2 \times 2^{1/2} {/eq}

    • {eq}2 {/eq}

    • {eq}2^2 {/eq}

    • {eq}2^{1/2} {/eq}

  • 10.

    The mean number of customers arriving at an auto repair shop has a Poisson distribution with a rate of 5 per hour. Find the variance of the number of arrivals in the first 30 minutes of an hour.

    Answers:

    • 2.5

    • 0

    • 5

    • 2

  • 11.

    Suppose the frequency of customers who arrive at KFC can be modeled using a Poisson process with a rate of 13 customers per hour. What is the variance for the frequency of customers in Rihana's 4 hour shift?

    Answers:

    • 13

    • 52

    • 92

    • 48

  • 12.

    Suppose that the number of English books that are issued from a library follows a Poisson process with a mean of 25 per day. Find the variance for the number of books taken in the next five days.

    Answers:

    • 25

    • 125

    • 5

    • 625

  • 13.

    The arrival of patients at a dentist follows the Poisson process with a rate of 0.15 per minute. Calculate the variance for the number of patients between 1:00 pm and 1:15 pm.

    Answers:

    • 2.25

    • 1.15

    • 22.5

    • 1.50

  • 14.

    Suppose a number of theft complaints received in a Police station follow a Poisson process with a mean of 2.5 per hour. Calculate the variance for the number of complaints received in a day.

    Answers:

    • 50

    • 30

    • 25

    • 60

  • 15.

    Assume the number of people being admitted to an ICU ward in a hospital can be modeled by a Poisson process with a mean of 1.2 per 3 hours. Find the variance for the number of people being admitted in 3 days.

    Answers:

    • 86.4

    • 10.8

    • 3.6

    • 28.8

  • 16.

    If a random variable x follows a Poisson distribution such that P(x = 0) = 0.7788 and rate parameter of 0.25, find the variance of x.

    Answers:

    • 2.50

    • 5.00

    • 0.25

    • 0.50

  • 17.

    The number of online registrations for an exam has a mean of 200 per ten minutes. Find the variance of the number of registrations in two hours.

    Answers:

    • 400

    • 2000

    • 1200

    • 2400

  • 18.

    The random variable X follows a Poisson distribution with parameter {eq}\lambda = 0.1 {/eq}. Calculate the variance for X.

    Answers:

    • 0.10

    • 10.00

    • 1.00

    • 0.01

  • 19.

    Assume that the number of monthly breakdowns of a water motor in a building can be modeled through a Poisson distribution with a parameter of 0.75. Calculate the variance for the number of breakdowns in that entire year.

    Answers:

    • 9

    • 12

    • 7.5

    • 10

  • 20.

    A study shows that the number of accidents that happen in 2 weeks at the main crossing road is 13. What is the variance for the entire month? (assuming 4 weeks in a month)

    Answers:

    • 6.5

    • 169

    • 26

    • 52

  • 21.

    A quality inspector in his report mentioned that there are 6 defective units in every lot, on average. If each lot contains 1000 articles and the company ordered 500 lots, then what is the variance of the defective articles in lots that are ordered?

    Answers:

    • 600

    • 5000

    • 1000

    • 3000

  • 22.

    In a research article, it is shown that on average 3 persons die every month due to car accidents. Find the variance for the number of deaths due to car accidents in that year.

    Answers:

    • 39

    • 26

    • 36

    • 30

  • 23.

    At a 24 hour call center, an average of 105 customers complains about the quality of certain products every day. If the number of complaints follows the Poisson distribution, then what is the variance for the number of complaints in the entire month?

    (Assume 30 days in the month)

    Answers:

    • 105x30

    • 105x24x7

    • 105x24

    • 1050x7

  • 24.

    On average, 16 vehicles pass a bridge per two hours. Find the variance for the number of vehicles passing through the bridge in 30 minutes.

    Answers:

    • 4

    • 8

    • 16

    • 12

  • 25.

    A water pipe has 3 defects per 100 meters, on average. If the number of defects follow a Poisson distribution, then find the variance for the number of defects per 1 km.

    Answers:

    • 300

    • 3

    • 30

    • 3000

  • 26.

    In a BPO, an executive answers 12 calls per hour. If he works for 8 hours, then what is the variance for the number of calls he attends?

    Answers:

    • 144

    • 96

    • 12

    • 36

  • 27.

    On average, 1.2 employees resign every month due to strict policies on leaves. If we assume that it can be modeled using the Poisson distribution, then calculate the variance for the number of resignations in 8 months.

    Answers:

    • 18.6

    • 8

    • 12

    • 9.6

  • 28.

    As per a report, on average, 10 out of 10,000 persons in a State have a certain disease. If it follows the Poisson distribution, then what is the variance for the number of people who have that disease if the state's population is 500,000?

    Answers:

    • 1000

    • 50

    • 500

    • 100

  • 29.

    A nurse mentioned that she attends 0.65 children per day who are afraid of injections. If we assume that this follows a Poisson process, then what is the variance for the number of children the nurse attends per 10 days who are afraid of injections?

    Answers:

    • 650

    • 0.65

    • 65

    • 6.5

  • 30.

    As per an instructor's report, on average 4 students fail a Statistics exam conducted once in 6 months. Calculate the variance as per his report for the number of students who failed in the last 10 years.

    (Assume that the number of students in the class remains the same)

    Answers:

    • 80

    • 60

    • 40

    • 240

Support