Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a random - Mathematics and Statistics

Sum

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has exactly 5 rats.

Advertisement Remove all ads

Solution

Let X denote the number of rats per bunglow.
Given, m = 5 and e–5 = 0.0067
∴ X ~ P(m) ≡ X ~ P(5)
The p.m.f. of X is given by

P(X = x) = `("e"^-"m" "m"^x)/(x!)`

∴ P(X = x) = `("e"^-5*(5)^x)/(x!), x` = 0, 1, ..., 5

P(exactly five rats)
= P(X = 5)

= `("e"^-5*(5)^5)/(5!)`

= `(0.0067 xx 5^5)/(5 xx 4 xx 3 xx 2 xx1)`

= `(0.0067 xx 625)/(24)`

= `(4.1875)/(24)`
= 0.1745

Concept: Poisson Distribution
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.4 | Q 1.07 | Page 152
Advertisement Remove all ads

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×