Question

The provincial governments are concerned with ruptures in towns (defined as being smaller that cities). For a certain category of town size, namely medium sized, ruptures occur at an average rate of 1 rupture per 200 town-years (if one is focusing on 1 of these towns, this implies that ruptures occur on average once every 200 years, if focusing on 10 such towns the rate will be increased by 10-fold). Assume that in the province of Ontario there are 800 such towns, and let the random variable X represent the number ruptures in a year occuring in the 800 medium sized towns. Calculate:

(a) (1 point) The expected value for X (b) (1 point) The standard deviation for X (c) (1 point) The coefficient of variation for X (d) (2 points) The probability that 4 or more ruptures occur in that year

Answer 1

Answer:

Given,

= 800*(1/200)

= 800/200

= 4

a)

E(X) =

= 4

b)

standard deviation S(X) = sqrt()

= sqrt(4)

= 2

c)

Coeff. of Variation = S(X) / E(X)

= 2 / 4

= 1/2

= 0.5

d)

P(X >= 4) = 1 - P(X <= 3)

= 1 - [P(0) + P(1) + P(2) + P(3)]

= 1 - [e^-4*4^0/0! + e^-4*4^1/1! + e^-4*4^2/2! + e^-4*4^3/3!]

= 1 - [0.0183 + 0.0733 + 0.1465 + 0.1954]

= 1 - 0.4335

= 0.5665