IITM BS Question 21 - Week 11 Practice

Prasnya

IITM BS Question 21 - Week 11 Practice | Prasnya

00:00

Q21Numerical4 Marks3 Sep 2023

The number of earthquakes in a region follows a Poisson distribution, with an average rate of 0.3 earthquakes per week. What is the probability that there will be no earthquake in the next 14 days? (Note: 1 week = 7 days) (Enter the answer correct to 2 decimal places.) With an average rate of 0.3 earthquakes per week, the mean number of earthquakes in a 2-week period is

\lambda

= 0.3 * 2 = 0.6. Using the Poisson PMF, P(X = k) = e^(-

\lambda

) *

\lambda

^k / k!: The probability of zero earthquakes (k = 0) in 14 days is:

P(X = 0)

= e^(-0.6) * 0.6^0 / 0! = e^(-0.6) ≈ 0.5488. Rounding to 2 decimal places gives 0.55 (accepted range: 0.52 to 0.58).

Your answer

Press Enter to check.

Q21

00:00

3 Sep 2023

Statistics 1 · Week 11

Q21.The number of earthquakes in a region follows a Poisson distribution, with an average rate of 0.3 earthquakes per week. What is the probability that there will be no earthquake in the next 14 days? (Note: 1 week = 7 days) (Enter the answer correct to 2 decimal places.) With an average rate of 0.3 earthquakes per week, the mean number of earthquakes in a 2-week period is

\lambda

= 0.3 * 2 = 0.6. Using the Poisson PMF, P(X = k) = e^(-

\lambda

) *

\lambda

^k / k!: The probability of zero earthquakes (k = 0) in 14 days is:

P(X = 0)

= e^(-0.6) * 0.6^0 / 0! = e^(-0.6) ≈ 0.5488. Rounding to 2 decimal places gives 0.55 (accepted range: 0.52 to 0.58).

Your Answer

Save

Check

Details