Question

8. The mean number of fatal accidents between Mile markers 0 and 40 is 5 per year.

What is the probability there are a) exactly 3 fatalities b) less than 5 fatalities, c) 4 or less fatalities d) greater than 4 fatalities, greater e) Between 1 and 4 fatalities (10 points)

a	b	c	d	e

Answer 1

Solution:-

The mean number of fatal accidents between Mile markers 0 and 40 is 5 per year.

a) The probability there are exactly 3 fatalities is 0.1404.

x = 3

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x = 3) = 0.1404

b) The probability there are less than 5 fatalities is 0.4405.

x = 5

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x < 5) = 0.4405

c) The probability there 4 or less fatalities is

x = 4

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x < 4) = 0.4405

d) The probability there are greater than 4 fatalities is 0.5595.

x = 4

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x > 4) = 0.5595

e) The probability there are between 1 and 4 fatalities is 0.4338.

x₁ = 1

x₂ = 4

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(1 < x < 4) = P(x > 1) - P(x > 4)

P(1 < x < 4) = 0.9933 - 0.5595

P(1 < x < 4) = 0.4338