Question

A A radar unit is used to measure speeds of cars on a motorway. the speeds are normally distributed with a mean of 90 km/her and a standard devaition of 10 Km/hr what is the presball lity that are at random is treavelling at more than lookm/hr

Answer 1

Let x be the random variable that represents the speed of cars.

x has μ=90,σ=10.

We have to find the probability that x is higher than 100 or P(x>100)

Given x,z=  

x−μ/σ

​ Thus for x=100,z=  10

100−90  =1

⇒P(x>100)=P(z=1)

= [total area]−[area to the left of z=1]

=1−0.8413 (from normal distribution table)

∴P(x>100)=0.1587

Hence the probability that a car selected at a random has a speed greater than 100 km/hr is equal to 0.1587.