Question

The following table contains the probability distribution for the number of traffic accidents daily in a small city:

Answer 1

Answer:

a) 2 accidents per day

b) .7071 accidents

Step-by-step explanation:

a) The mean is the sum of each possible number of accidents multiplied by its respective probability. So,

E(x) = (0)(.1) + (1)(.2) + (2)(.45) + (3)(.15) + (4)(.05) + (5)(.05) = 2

b) The variance V(x) = E(x^2) - E(x)^2, and the standard deviation is the square root of the variance. So,

V(x) = E(x^2) - (2)^2

= (0)(.1) + (1)(.2) + (4)(.45) + (9)(105) + (16)(.05) + (25)(.05) - 4 = 0.5

sqrt(0.5) = .7071