Question

The probability of being in a car accident when driving more than 10 miles over the speed limit in a residential neighborhood is 0.07. of the next 1,698 cars that pass through a particular neighborhood, what are the first and third quartiles for the number of car accidents in this neighborhood?

Answer 1

We are given the following values:

n = number of samples / cars = 1,698

p = probability of each success = 0.07

 

The standard deviation (σ) is calculated using the formula:

σ = sqrt [n p (1 – p)]

σ = sqrt [1,698 (0.07) (1 – 0.07)]

σ = 10.51

 

The mean (x) is:

x = n p

x = 1,698 (0.07)

x = 118.86 car accidents

 

The quartiles are:

1st quartile = x - 2σ to x – σ

1st quartile = 118.86 – 2 (10.51) to 118.86 – 10.51

1st quartile = 97.84 to 108.35

(97.84<Q1<108.35)

 

3rd quartile = x to x + σ

3rd quartile = 118.86 to 118.86 + 10.51

3rd quartile = 118.86 to 129.37

(118.86<Q3<129.37)