Question

A radar unit is used to measure speeds of a car on a motorway. Speeds are normal distributed with a mean of 90 km an hour and a standard deviation of 10 km an hour. What is the probability that a car picked at random is traveling out more than 100 km an hour

Answer 1

let x is the random variable that represents the speed of car.

probability that x is higher than 100 :

`P(x>100)`

for x=100:

`\begin{gathered} z=(x-\mu)/(\sigma) \\ z=(100-90)/(10) \\ z=1 \end{gathered}`

so,

`p(x>100)=p(z=1)`

probability =total area - area of the left of (z=1)

`\begin{gathered} \text{probability}=1-0.8413 \\ p(x>100)=0.1587 \end{gathered}`

and the area of the left of z=1 is 0.8413 (from normal distribution)